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<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>Dear Michel and All,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>I cannot show you a single
definition of order or disorder. Perhaps the best place to start is with the
origin of the English word ‘order’ (Latin: <i><span
style='font-style:italic'>ordo</span></i>) which refers to the sequence of
threads in the woof of a weaving. Different sequences are perfectly clear
phenomenologically, no? It also seems to me that such an ‘order’ is
a quite limited scalar quantity.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>I would like to
propose that order and disorder cannot in fact be defined independently of one another.
Any sequence of threads which has been <i><span style='font-style:italic'>changed
</span></i>is a disorder relative to the initial state. The notion of change
clarifies the problem further, because any non-random change requires an operator,
who is capable of reversing the process, replacing the threads in their initial
sequence. <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>I conclude,
following Michel, that the answers to questions of maximal and minimal order
defined as a scalar will be the same as those for any other scalar quantity. <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>However,
characterization of a dynamic concept of order, where order is not a scalar
quantity but can have qualitative properties, is possible but requires
reference to the evolution of some process, that is, to change. One could
define regions where the sequences are stable or unstable (actually or
potentially being changed), but also pleasing or displeasing <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>We can then expect
that the laws of this kind of ‘order’ will follow a
non-Kolmogorovian probability distribution, be difficult to define and impossible
to compute. That’s life.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>Cheers,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Lucida Sans Unicode"><span lang=EN-US
style='font-size:11.0pt;font-family:"Lucida Sans Unicode"'>Joseph <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>-----Original Message-----<br>
From: Fis [mailto:fis-bounces@listas.unizar.es] On Behalf Of Michel Petitjean<br>
Sent: lundi, 4 janvier 2021 20:48<br>
To: Arieh Ben-Naim<br>
Cc: fis<br>
Subject: Re: [Fis] Fwd: Entropy, the Second Law, and Life</span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Dear Arieh,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Many thanks for your great contribution.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Eisnstein was right, the framework of applicability is
the main point.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>And it is often neglecetd, about the universe, and
about life.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>We can find in many books about thermodynamics a
definition of entropy.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>I don't discuss it, even if there is much to say about
it.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>An important point is, what is disorder?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Does anybody can show me a definition of disorder?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>May be the negation of order.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>But what is order ?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Not the mathematical definition in set theory (partial
order, total<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>order), it seems to be something else.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Does anybody can show me a definition of order?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>If somebody can tell me what is order or what is
disorder<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>(microstates? randomness? else?), my next question
follows.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Is it possible to define what is the maximal order (or
minimal<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>disorder), and conversely, what is the minimal order
(or maximal<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>disorder)?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Once we get clear concepts in simple situations, we
may discuss their<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>application to life.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>If the concepts are unclear in simple situations,
disussing their<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>application to life will never end.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Best regards,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Michel.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Michel Petitjean<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Université de Paris, BFA, CNRS UMR 8251, INSERM ERL
U1133, F-75013 Paris, France<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Phone: +331 5727 8434; Fax: +331 5727 8372<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>E-mail: petitjean.chiral@gmail.com (preferred),<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> michel.petitjean@univ-paris-diderot.fr<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>http://petitjeanmichel.free.fr/itoweb.petitjean.html<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Le lun. 4 janv. 2021 ŕ 19:03, Arieh Ben-Naim
<ariehbennaim@gmail.com> a écrit :<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> ---------- Forwarded message ---------<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> From: Pedro C. Marijuan <<st1:PersonName
w:st="on">pcmarijuan.iacs@aragon.es</st1:PersonName>><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Date: Sat, Jan 2, 2021 at 8:57 PM<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Subject: Entropy, the Second Law, and Life<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> To: Arieh Ben-Naim <ariehbennaim@gmail.com><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Dear FIS Discussants,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> It is for me a great pleasure to impart this New
Year Lecture. I will address one of my favorite topics: the numerous and
notable misunderstandings that historically have accompanied, and continue to
accompany, the relationship between entropy and life. I have devoted many years
to the study of entropy and produced quite a few books and articles about that
(see the references below). It is amazing the persistence of so many errors,
misunderstandings and blunders around that fundamental concept. As a guide to
the present discussion, I have attached a chapter of my new book on
"Entropy: The greatest Blunder in the History of Science". In the
excerpt that follows herein, I have dropped most of the formal arguments, so
let me emphasize reading the entire chapter --sent in a separate mail (for
list-server reasons).<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Best wishes<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Arieh<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Entropy, the Second Law, and Life<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Arieh Ben-Naim<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Emeritus Professor, Department of Physical
Chemistry, The <st1:PlaceName w:st="on">Hebrew</st1:PlaceName> <st1:PlaceType
w:st="on">University</st1:PlaceType> of <st1:City w:st="on"><st1:place w:st="on">Jerusalem</st1:place></st1:City><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Introduction<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> I would like to start this article with a
quotation by Albert Einstein on thermodynamics:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “It is the only physical theory of
universal content, which I am convinced, that within the framework of
applicability of its basic concepts will never be overthrown.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Most people who use this quotation, emphasize the
last part, namely, that Thermodynamics will “never be overthrown.”
Of course I agree with that part. However, my emphasis, in this article is on
the “framework of applicability.” My main point is that entropy and
the Second Law were used far beyond their “framework of
applicability.” One such application is to living systems, which I will
discuss in this article. The second is the application of Entropy and the
Second Law to the entire universe. This is discussed in details in references
[1,2].<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> The application of entropy and the Second Law to
a living system is based on two erroneous assumptions:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 1. Entropy is a measure of disorder (or
disorganization)<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Life is understood as a process towards organization
and creation of order<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> From these two assumptions it follows, almost
naturally that life-processes seem to be “a struggle against the Second
Law of Thermodynamics.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In this article we shall distinguish between two
different questions: The first one, the possibility of defining entropy; and
the second, the applicability of the Second Law to living systems. We shall
start with the general question on whether one can or cannot describe a living
system by a few thermodynamic variables such as temperature, pressure and
composition. This discussion will lead us to conclude that one cannot specify
the “thermodynamic state” of a living system. It follows that
entropy is undefinable for any living system. Next, we shall discuss the question
of the applicability of the Second Law to living systems. The answer to this
question is a definite, No!<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Can entropy be defined for any living system?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> This question is part of a more general question:
Can physics, as we know it today, be used to discuss and explain all aspects of
life? In particular, those aspects of life we call mental processes such as
thinking, feeling, consciousness, and the like. This question has been
discussed by numerous scientists, in particular by Schrödinger [3], Penrose
[4,5] and many others. Interestingly, some of these scientists raised serious
doubts about the general question stated above, yet they did not shy away from
applying entropy and the Second Law to living systems.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Everyone knows that life phenomena are the most
complex, intricate, interesting, wonderful, and whatever one wishes to ascribe
to it. During the 20th century science had achieved a great amount of knowledge
and understanding about the many aspects of life, from biochemical processes,
genetics, molecular biology, to brain functions, and many more. There are
however many more aspects of life that we do not understand. There are also
aspects of life that we might never understand.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Indeed, during the past century remarkable
advances in understanding the molecular basis of life have been achieved. A
whole new branch of biology was created: Molecular Biology. The mechanism of
heredity was deciphered, the so-called “genetic code” was
discovered, the code which is responsible for translating the message “written”
in the DNA into synthesizing proteins which are the so-called molecular robots
in our cells.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> There are many specific processes which have been
studied by thermodynamics. Examples: Chemical reactions, including metabolism
where energy stored in some chemical bonds are used to synthesize many
molecules which are vital to life. Photosynthesis, where energy from the sun
rays is used to convert carbon dioxide (CO2) and water (H2O) to high energy
sugars. In all of these cases the reactions could be studied in vitro, i.e. in
a laboratory setting, or in test tubes, isolated from the entire complicated
environment in the cell (in vivo). Clearly, thermodynamics was, and still is,
the main tool in understanding the energetics of these reactions.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> There are other processes such as muscle
contraction (i.e. converting chemical energy into mechanical work) or
“firing” of electrical signals along the nerves’ axons which
were studied thoroughly by thermodynamics and statistical mechanics. In all of
these specific processes one can isolate the process and study it in
well-defined environments and apply all the tools of thermodynamics
successfully. However, with all these remarkable achievements which fill up
countless textbooks on molecular biology, biochemistry, energy transduction,
neural networks and more, there is still one phenomenon that was, and still is,
inaccessible to study with the tools of thermodynamics in particular, and in
physics, in general. This is life itself.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In fact, we still do not know how to define
“life” or life related phenomena such as consciousness, awareness,
the mechanism underlying our thinking, our feelings, and our ability to make
decisions or create arts. Notwithstanding the difficulty of defining
“life,” it is clear that a living system is far from equilibrium.
As such the concept of entropy cannot be applied. Simply because entropy is a
state function. This means that entropy is definable for a well-defined
thermodynamic system at equilibrium.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> We can easily describe the “state” of
person sitting in a room. But this is not a thermodynamic description which
requires just a few thermodynamic parameters. However, even if we could
describe the physical state of the body, there is still the question of how to
describe the state of the mind of the person? The last question brings us to
the classical question about the nature of the mind. It is possible that within
some future extensions of physical theories all mental activities could be
discussed. However, at this point in time it is appropriate to be cautious and
refer to this possibility as a “hypothesis.” In my view, statements
such as Crick’s “Astonishing Hypothesis” is very much a
hypothesis, and it will remain a hypothesis for a long time. If and when this
hypothesis will be proven to be correct, then it will be an enormously
astonishing achievement, particularly to all those who subscribe to the concept
of dualism.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> To conclude, we do not know whether or not living
systems can be described as purely material objects on which all the physical
laws are applicable. But even if such a description becomes feasible, one could
not claim that living systems are well-defined thermodynamic systems, i.e.
macro-systems describable by a few thermodynamic variables. Therefore, entropy
may not be applied to such systems. This conclusion very clearly follows from
any definition of entropy See Ben-Naim [1,2,8-10].<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> The history of application of Entropy and the
Second Law to living systems<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Perhaps the oldest association of Second Law with
life is due to Boltzmann. On May 29, 1886, Ludwig Boltzmann presented a talk at
the Festive Session of the Imperial Academy of Sciences in <st1:City w:st="on"><st1:place
w:st="on">Vienna</st1:place></st1:City> where he discussed “The Second
Law of Thermodynamics” with special emphasis on its application in
relation to Charles Darwin's 1859 theory of evolution [16].<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> The most-quoted passage from this lecture is that
life is a struggle for entropy:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “The general struggle for existence of
animate beings is not struggle for raw materials, these, for organisms, are
air, water and soil, all abundantly available, nor for energy, which exists in
plenty in anybody in the form of heat Q, but of a struggle for entropy, which
becomes available through the transition of energy from the hot sun to the cold
earth.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> As we have discussed above (see attached
Chapter), Boltzmann believed that a system proceeds from a low to a high
probability, also he stated that systems proceed from ordered to disordered
states. Since living systems are considered to proceed from disorganized to
more organized he has used essentially the argent in the abstract to conclude
that life is a “struggle for entropy”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> However, the most influential physicist who
propagated the erroneous ideas about entropy and life was Erwin Schrödinger. In
his book “What is Life?” published in (1944) [3], he discussed in
greater detail the role of entropy in living systems. We will provide some
quotations from this book in the next section.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Schrödinger’s book: What is life?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> On the question: “What is life? one cannot
avoid starting with the most famous book written by Schrödinger [3].<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> This book is based on lectures delivered by
Schrödinger in <st1:City w:st="on"><st1:place w:st="on">Dublin</st1:place></st1:City>
in 1943. This book was most influential for a long time and probably laid the
cornerstone for the creation of the whole field of molecular biology. It also
has encouraged many physicists to apply the methods of physics to biology. In
this section we shall present only a few comments about some of
Schrödinger’s statement regarding entropy, more details may be found in
reference [2].<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In Chapter 1 of his book, Schrödinger correctly
pointed out that “the physicist’s most dreaded weapon, mathematical
deduction, would hardly be utilized. The reason for this was not that the
subject was simple enough to be explained without mathematics, but rather it
was too much involved to be fully accessible to mathematics. As I noted above,
it is not clear at all which kind of mathematics or physics one would need to
describe life. Then Schrödinger outlines the plan of his lectures as follows:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “The large and important and very much
discussed question is: How can the events in space and time which take place
within the spatial boundary of a living organism be accounted for by physics
and chemistry?”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> His preliminary answer to this question:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “The preliminary answer which this little
book will endeavor to expound and establish can be summarized as follows: The
obvious inability of present-day physics and chemistry to account for such
events is no reason at all for doubting that they can be accounted for by those
sciences.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Schrödinger attempts to explain the source of
difficulty of applying the methods of physics and chemistry to living systems.
The fundamental difference between a living system and any piece of matter that
physicists and chemists have ever handled is in the structure, or the
arrangement of atoms and molecules in the organism differs fundamentally from
that of a system dealt with physics and chemistry. It seems to me that
Schrödinger, at least in this stage of the book believed that once physicists
enter into biology and apply their powerful arsenal of physical methods and
theories, they shall be able to answer the question posed in the book.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> On page 10 Schrödinger provides some hints about
his intention to use the Second Law:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “The reason for this is, that what we call
thought (1) is itself an orderly thing, and (2) can only be applied to
material, i.e. to perception or experiences, which have a certain degree of
orderliness… Therefore, the physical interactions between our system and
others must, as a rule, themselves possess a certain degree of physical
orderliness, that is to say, they too must obey strict physical laws to a
certain degree of accuracy.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> My impression is that Schrödinger used the terms
“orderly thing,” “orderliness,” “physical organization,”
“well ordered organization,” and similar terms in anticipation of
his usage of entropy and the Second Law of thermodynamics in later chapters.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Chapter 6, of his book is titled: “Order,
disorder and entropy.” He starts with the common and erroneous statement
of the Second Law in terms of the “order” and
“disorder.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “It has been explained in Chapter 1 that
the laws of physics, as we know them, are statistical laws. They have a lot to
do with the natural tendency of things to go over into disorder.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> There is of course, no such “natural
tendency,” except in the minds of those who have a distorted view of the
Second Law. Then, he makes another typical statement about life:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Life seems to be orderly and lawful behavior of
matter, not based exclusively on its tendency to go over from order to
disorder, but bases partly on existing order that is kept up.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> The idea that life somehow withstands the
“natural tendency to go from order to disorder” is quite frequently
found in the literature;” “life withstands the ravages of
entropy,” “life disobeyed the Second Law” and so on.
Unfortunately, all these statements are meaningless; there exists no tendency
of going from order to disorder in the first place. The tendency of entropy to
increase applies to some specific processes in isolated systems, and not to a
living system which is an open system, far from equilibrium. It is only on page
74 that he explicitly relates the Second Law with the behavior of living
systems.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “The general principle involved is the
famous Second Law of Thermodynamics (entropy principle) and its equally famous
statistical foundation.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> His main claim is that “living matter
evades the decay to equilibrium.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “It is avoiding the rapid decay into the
inert state of ‘equilibrium’ that an organism appears to be
enigmatic; so much so, that from the earliest times of human thought some
special non-physical or supernatural force (vis viva, entelechy) was claimed to
be operative in the organism, and in some quarters is still claimed.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Then he asks:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “How does the living organism avoid decay?
The obvious answer is: By eating, drinking, breathing and (in the case of
plants) assimilating. The technical term is metabolism.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> I believe that the book’s highlight is
reflected on page 76:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “What then is that precious something
contained in our food which keeps us from death? That is easily answered. Every
process, event, happening – call it what you will; in a word, everything
that is going on in Nature means an increase of the entropy of the part of the
world where it is going on. Thus, a living organism continually increases its
entropy – or, as you may say, produces positive entropy – and thus
tends to approach the dangerous state of maximum entropy, which is death. It
can only keep aloof from it, i.e. alive, by continually drawing from its
environment negative entropy – which is something very positive as we
shall immediately see. What an organism feeds upon is negative entropy. Or, to
put it less paradoxically, the essential thing in metabolism is that organism
succeeds in freeing itself from all the entropy it cannot help producing while
alive.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> First, I certainly do not agree that everything
that goes on in Nature means an “increase of the entropy,” second,
that living things “produce positive entropy,” and finally that the
only way it can keep alive is by drawing negative entropy from its environment.
I, of course realize that such assertions have been made by numerous
scientists. Unfortunately, none of these can be justified in terms of the
entropy and the Second Law. Such statements, in my opinion are meaningless.
Entropy, by definition, is a positive quantity. There is no negative entropy,
as there is no negative volume, negative mass or negative time.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Did Schrödinger have a bad slip of the tongue in
this statement? It seems to me that Schrödinger did believe in what he said. It
is unfortunate however, that many others, scientists as well as non-scientists
fell into the pitfall created by Schrödinger’s negative entropy. On page
78 Schrödinger concludes that “organization is maintained by extracting
order from the environment.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “Living organism… delays the decay
into thermodynamic equilibrium (death), by feeding upon negative entropy,
attracting a stream of negative entropy upon itself… and to maintain
itself on a stationary and fairly low entropy level.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Since there is no way of measuring or calculating
the “entropy level” of a living system, all these impressive
statements are outright meaningless. They certainly do not answer the question
posed in the title of Schrödinger’s book.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In concluding, Schrödinger’s book was no
doubt a very influential one especially in encouraging many physicists to look
into biology. Most people praised the book, but some expressed their doubts
about its content.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Perhaps, the most famous skeptic of
Schrödinger’s contribution to understanding of life, was Linus Pauling.
In Hager’s (1995) biography of Linus Pauling, he wrote about
Pauling’s view about Schrödinger’s book [17].<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “Pauling thought the book was hogwash. No
one had ever demonstrated the existence of anything like “negative
entropy… Schrödinger’s discussion of thermodynamics is vague and
superficial… Schrödinger made no contribution to our understanding of
life.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> I fully agree!<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Likewise, Perutz had a similar criticism of
Schrodinger’s book, in 1987) [18]:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “When I was invited to review the influence
of What is Life? I accepted with the intention of doing honor to Schrodinger's
memory. To my disappointment, a close study of his book and of the related
literature has shown me that what was true in his book was not original, and
most of what was original was known not to be true even when it was written.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In conclusion, in my view both comments by
Pauling and Perutz were quite mild. Regarding the involvement of entropy and
the Second Law, I feel that Schrödinger has miserably gone astray. In general,
I was disappointed with his book. My main reason is not because Schrödinger did
not offer an answer to the question posed in the title of the book, but because
whatever partial answers he offered are at best unconvincing and perhaps even
meaningless.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> I should also add one personal comment about the
very idea of invoking entropy and the Second Law in connection with life
phenomena. Personally, I believe that if ever a “complete theory of
life” will be available, it will involve neither entropy nor the Second
Law of thermodynamics. In light of this belief, I think that
Schrödinger’s book has unintentionally encouraged people in making a lot
of meaningless statements associating entropy and the Second Law with life
phenomena.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> More on Entropy, the Second Law and life<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Open any book discussing the question of
“What is Life?” and you are likely to read grandiose statements
ranging from “life violates the Second Law of Thermodynamics,” to
“life emerges from the Second Law,” and that the Second Law
explains many aspects of life, perhaps life itself.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> The involvement of the Second Law in life is
based on the misconstrued (I would even say, perverted) interpretation of
entropy as a measure of disorder, on one hand, and the view that life is a
process towards more order, more structure, more organization, etc. on the
other hand.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Combining these two erroneous views inevitably
leads us to the association of life phenomena with a decrease in entropy. This
in turn leads to the erroneous (perhaps meaningless) conclusion that life is a
“struggle” against the Second Law. I should add that even if the
two assumptions were correct, the conclusion will still be wrong! The fact is
that entropy cannot be defined forany living system, and the Second Law, in its
entropy formulation does not apply to living systems.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Here is an example from Katchalsky[19] in (1963):<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “Life is a constant struggle against the
tendency to produce entropy by irreversible process. The synthesis of large and
information-rich-macromolecules…all these are powerful anti-entropic
force…living organism choose the least evil. They produce entropy at a
minimal rate by maintaining a steady state.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> This is a beautiful statement but devoid of any
meaning. No one knows how to define the entropy of a living system, and how
much entropy is produced by a living organism.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Volkenstein [20], comments on the
“anti-entropic” by saying:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “At least we understand that life is not
“antientropic,” a word bereft of meaning. On the contrary, life
exists because there is entropy, the export of which supports biological
processes…”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Indeed “anti-entropic” is as
meaningless as “anti-volume,” (see also reference [2]).
Unfortunately, Volkenstein’s statement is far more meaningless than the
concept of “anti-entropic.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Here is another outstanding example:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In Atkins’ (1984) introduction to his book
[11] he writes:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “In Chapter 8 we also saw how the Second
Law accounts for the emergence of the intricately ordered forms characteristic
of life.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Of course, this is an unfulfilled promise. No one
has ever shown that the Second Law accounts for the emergence of… life!
At the end of Chapter 7, Atkins writes:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “We shall see how chaos can run apparently
against Nature, and achieve that most unnatural of ends, life itself.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Finally, after discussing some aspects of
processes in a living organism, Atkins concludes his book:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “We are the children of chaos, and the
deep structure of change is decay. At root, there is only corruption, and the
unstemmable tide of chaos… This is the bleakness we have to accept as we
peer deeply and dispassionately into the heart of the universe.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Yet, when we look around and see beauty, when we
look within and experience consciousness, and when we participate in the
delights of life, we know in our hearts that the heart of the universe is
richer by far.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> So beautiful and so empty combination of words!<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Do we feed on negative entropy?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Brillouin [21], “feeding on the negative
entropy” ideas pronounced by Schrödinger, goes even further and claims
that:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “If living organism needs food, it is only
for the negentropy it can get from it, and which is needed to make up for the
losses due to mechanical work done, or simple degradation processes in living
systems. Energy contained in food does not really matter: Since energy is
conserved and never gets lost, but negentropy is the important factor.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> This is quite strange. If this is the case, why
do all food products reflect caloric value on their labels? The food
manufacturers should instead print the “important factor” of
negentropy in units of calories per degree or perhaps in bits, on their labels.
Thus, next time you look at the labels on food products you can ignore the
“energy value” as they are not important. What matters and the only
important information to watch out for is the meaningless negentropy!<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> While I am still baffled with the concept of
negative entropy, or its shorter version negentropy, I was greatly relieved to
read Hoffmann’s [22] explanation:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “Life uses a low-entropy source of energy
(food or sunlight) and locally decreases entropy (created order by growing) at
the cost of creating a lot of high-entropy “waste energy (heat and
chemical waste).”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In more modern books the meaningless notion of
negative entropy (or neg-entropy) is replaced by the more meaningful term of
low entropy.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Is it meaningful to claim that we, living
organisms feed on low entropy food?<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> If you are convinced that feeding on low entropy
food is the thing that keeps you alive you should take your soup (as well as
your coffee and tea) as cold as possible. This will assure you of feeding on
the lowest possible liquid food. As for solid food, you should try to eat
frozen food (but be careful not to put anything at very low temperatures into
your mouth, that’s going to be very dangerous). As we have noted before,
the entropy of a living system is not defined – not yet, or perhaps
never. The main reason is that we do not know how to define the state of a
living system.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> In a recent book by Rovelli [23], the nonsensical
idea that “entropy is more important than energy is elevated to highest
peak. You will find there a statement written in all capital letters:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “IT IS ENTROPY, NOT ENERGY THAT DRIVES THE
WORLD”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> This very sentence has been praised by some of
Rovelli’s reviewers. Here, I will briefly say that the entropy of the
universe (or the world) is not definable. Therefore, entropy does not, and
cannot drive the universe. In fact, (yes, it is a fact) entropy does not drive
anything, not even processes in systems for which the entropy is defined.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Besides this nonsensical statement, Rovelli goes
on to discuss the idea of living beings feeding on low entropy. In another
copycat statement which is attributed to Schrödinger, he suggests something
which I think is deceiving, irresponsible and dangerous. On page 164 he writes:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> “If all we needed was energy rather than
entropy, we would head for the heat of the <st1:place w:st="on">Sahara</st1:place>
rather than toward our meal.”<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> First, I think it is unfair (to say the least) to
say “if all we needed was energy.” No one needs only energy. We
need energy, for certain, but we also need some minerals, vitamins, and more
than anything, water is essential for our general well-being. For the sake of
argument, suppose that we already have everything, and all the rest we need is
energy. But then, the author suggests that one should head for the heat of the <st1:place
w:st="on">Sahara</st1:place>.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> This comment is dangerous because the energy that
we need is energy stored in some chemical compounds, not the “heat of the
<st1:place w:st="on">Sahara</st1:place>.” If one were to believe that
energy is important (and assuming that all other things including water, are
available) then going to the <st1:place w:st="on">Sahara</st1:place> instead of
having the next meal, will kill you, so better not to heed the Rovelli’s
advice.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Besides, the danger of the author’s
suggestion is also an absurd one. As I wrote above if you believe that entropy
is more important than the energy of food, then you should drink water as cold
as possible (preferably iced) which has a lower entropy than hot water. To
paraphrase the author’s suggestion (not to be taken seriously), I would
say that if all we need is entropy rather than energy, we should head for the
cold arctic rather than towards our next meal. I repeat that this is just to
paraphrase the author’s statement. I am not really suggesting that you do
it.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> If you swallow a cube of ice at 0 , or drink the
equivalent amount of liquid water at 0 , you will get the same benefit from the
water molecules. If you have a choice between the two options I recommend
drinking water (with a higher entropy) rather than the ice (with the lower
entropy), not because of the entropy difference between the two, but simply
because the latter might get stuck in your throat.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> To conclude this section, it should be stressed
that my objection to the usage of entropy and the Second Law applies to the
entire living system and the whole life phenomena. There is no objection to
studying specific chemical, mechanical, or electrical processes occurring
within a living system. However, phenomena involving mental or conscious
activities cannot be included in such process.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Some concluding remarks on Entropy, the Second
Law and Life<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> A great deal of knowledge (or information) has
been accumulated on many aspects of life. Yet, there is one aspect of life
which is elusive and that is, life itself. We do not know how to define life,
how life was created and whether or not life succumbs to the laws of physics.
Specifically, we do not know how to describe the state of being
“alive,” for any living organism. We can tell when something is
alive or not alive, but we cannot specify these states in any of the available
physical terms. Therefore, there is no point of applying the concept of
entropy, or of the Second Law to a living system.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> We can still apply the concept of information
both in its colloquial sense, and in its informational theoretical sense. In
spite of many claims in the literature, the information we have about life is
in general, not measurable. On the other hand, we can use the Shannon Measure
of information (SMI) to many probability distributions associated with living
systems. We can define the probability distribution of compounds in a cell, in
an organ, or in the entire organism. We can assign distribution to the letters
in the DNA or the letters of proteins, and so on. To each of these
distributions we can define the corresponding SMI. All these SMI are
well-defined quantities but they are not entropy. Entropy, when viewed as a
particular case of a SMI is defined for a specific distribution at a specific
state of equilibrium. We know that a living system is not an equilibrium state.
We do not know whether a living system tends to an equilibrium state, and
whether it will ever reach an equilibrium state. Therefore, as long as a living
system is alive, it is meaningless to apply to it the concept of entropy, nor
the Second Law of thermodynamics. It also follows that life does not violate
the Second Law, nor does it emerge from the Second Law. The Second Law does not
apply to a living system.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> At this stage of our knowledge of life we can be
satisfied with applying the SMI to well specified distribution functions
associated with a living system.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Unfortunately, we do not know whether or not the
SMI or information theory can be applied to life itself. Certainly, it cannot
be applied to explain aspects of life that are far from being understood such
as consciousness, thoughts, feelings, creativity, etc. Yet again, statements claiming
that information theory can help us with the comprehension of these aspects of
life abound in the literature. These statements are no doubt very impressive,
but unfortunately they are far from being true.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> References<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 1. Ben-Naim, A. (2016), Entropy the Truth the
Whole Truth and Nothing but the Truth, World Scientific <st1:place w:st="on"><st1:City
w:st="on">Publishing</st1:City>, <st1:country-region w:st="on">Singapore</st1:country-region></st1:place><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 2. Ben-Naim, A. (2020), The Greatest Blunder in
the History of Science, involving Entropy, Time, Life and the Universe. Independently
Publisher, Amazon.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 3. Schrödinger (1944), What Is Life? : The
Physical Aspect of the Living Cell, Based on lectures delivered under the
auspices of the Dublin Institute for Advanced Studies at Trinity College,
Dublin, in February 1943<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 4. Penrose, R. (1989), The Emperor’s Mind.
Concerning Computers, Minds and the Law of Physics, Penguin Books, <st1:State
w:st="on"><st1:place w:st="on">New York</st1:place></st1:State><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 5. Penrose, R. (1994)Penrose, R. (1994), Shadows
of the Mind: An Approach to the Missing Science of Consciousness, <st1:PlaceName
w:st="on">Oxford</st1:PlaceName> <st1:PlaceType w:st="on">University</st1:PlaceType>
Press, <st1:City w:st="on"><st1:place w:st="on">Oxford</st1:place></st1:City><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 6. Crick, F. (1994), “The Astonishing
Hypothesis,” The Scientific Search For the Soul,” Touchstone, Simon
and <st1:place w:st="on"><st1:City w:st="on">Shuster</st1:City>, <st1:State
w:st="on">New York</st1:State></st1:place><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 7. Dennett, D. (2017), “From Bacteria to
Bach and Back,” The Evolution of Minds,” W. W. Norton, Inc. USA,
Henry Holt and Co., <st1:State w:st="on"><st1:place w:st="on">New York</st1:place></st1:State>
(2018)<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 8. Ben-Naim, A. (2017), The Four Laws that do not
drive the Universe, World Scientific Publishing, <st1:country-region w:st="on"><st1:place
w:st="on">Singapore</st1:place></st1:country-region><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 9. Ben-Naim A. and Casadei D. (2017), Modern
Thermodynamics, World Scientific <st1:place w:st="on"><st1:City w:st="on">Publishing</st1:City>,
<st1:country-region w:st="on">Singapore</st1:country-region></st1:place><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 10. Ben-Naim, A. (2018), Time’s Arrow?The
Timeless Nature of Entropy and the Second Law of Thermodynamics. Lulu
Publishing Services<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 11. Atkins, P. (1984),The Second Law, Scientific
American Books, W. H. Freeman and Co., <st1:State w:st="on"><st1:place w:st="on">New
York</st1:place></st1:State><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 12. Atkins, P. (2007), Four Laws That Drive The
Universe, <st1:place w:st="on"><st1:PlaceName w:st="on">Oxford</st1:PlaceName> <st1:PlaceType
w:st="on">University</st1:PlaceType></st1:place> Press<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 13. Brush, S. G. (1976), The Kind of Motion We
Call Heat. A History of the Kinetic Theory of Gases in The 19th Century, Book
2: Statistical Physics and Irreversible Processes. North-Holland Publishing
Company<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 14. Brush, S. G. (1983), Statistical Physics and
the Atomic Theory of Matter, from Boyle and <st1:City w:st="on"><st1:place
w:st="on">Newton</st1:place></st1:City> to Landau and Onsager. <st1:PlaceName
w:st="on">Princeton</st1:PlaceName> <st1:PlaceType w:st="on">University</st1:PlaceType>
Press, <st1:place w:st="on">Princeton</st1:place>.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 15. Ben-Naim, A. (2020),Time for Everyone and
Time for Everything, Independent Publisher, Amazon<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 16. Boltzmann, L. (1877), <st1:place w:st="on"><st1:PlaceName
w:st="on">Vienna</st1:PlaceName> <st1:PlaceType w:st="on">Academy</st1:PlaceType></st1:place>.
42, “Gesammelte Werke” p. 193.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 17. Hager, T. (1995), Forces of Nature, the Life
of Linus Pauling, Simon and <st1:place w:st="on"><st1:City w:st="on">Schuster</st1:City>,
<st1:State w:st="on">New York</st1:State></st1:place><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 18. Perutz, M.F. (1987),Physics and the riddle of
life, Nature, 326, 555–558<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 19. Katchalsky, A. (1963), Nonequilibrium
Thermodynamics, Int. Sci. Technol, 43<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 20. Volkenstein, M. V. (2009), Entropy and
Information, translated by A. Shenitzer and A. G. Burns, <st1:place w:st="on"><st1:City
w:st="on">Birkhauser</st1:City>, <st1:State w:st="on">Berlin</st1:State></st1:place><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 21. Brillouin, L. (1962), Science and Information
Theory, Academic Press, <st1:State w:st="on"><st1:place w:st="on">New York</st1:place></st1:State><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 22. Hoffman, P.M. (2012), Life’s Ratchet,
How Molecular Machines Extract Order from Chaos, Basic Books, <st1:State w:st="on"><st1:place
w:st="on">New York</st1:place></st1:State><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 23. Rovelli, C. (2018) The Order of Time,
Riverhead books, <st1:State w:st="on"><st1:place w:st="on">New York</st1:place></st1:State><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 24. Styer, D.F. (2008), Entropy and Evolution,
Am. Journal of Physics, 76, 1031<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> 25. Sanford, J. C. (2005), Genetic Entropy and
the Mystery of the Genome, Ivan Press, a division of Elim Publishin<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> --<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> -------------------------------------------------<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Pedro C. Marijuán<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Grupo de Bioinformación / Bioinformation Group<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> <st1:PersonName w:st="on">pcmarijuan.iacs@aragon.es</st1:PersonName><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> http://sites.google.com/site/pedrocmarijuan/<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> -------------------------------------------------<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> --<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Prof. Arieh Ben-Naim<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Department of Physical Chemistry<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> The <st1:PlaceName w:st="on">Hebrew</st1:PlaceName>
<st1:PlaceType w:st="on">University</st1:PlaceType> of <st1:City w:st="on"><st1:place
w:st="on">Jerusalem</st1:place></st1:City><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> <st1:City w:st="on"><st1:place w:st="on">Jerusalem</st1:place></st1:City>,
91904<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> <st1:country-region w:st="on"><st1:place w:st="on">Israel</st1:place></st1:country-region><o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> _______________________________________________<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Fis mailing list<o:p></o:p></span></font></p>
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style='font-size:10.0pt'>> Fis@listas.unizar.es<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>>
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
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<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER
PERSONAL<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Ud. recibe este correo por pertenecer a una lista
de correo gestionada por la Universidad de Zaragoza.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
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w:st="on"><st1:place w:st="on">como</st1:place></st1:City> tratamos sus datos
en el siguiente enlace:
https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> Recuerde que si está suscrito a una lista
voluntaria Ud. puede darse de baja desde la propia aplicación en el momento en
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<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> http://listas.unizar.es<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>> ----------<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>_______________________________________________<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Fis mailing list<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Fis@listas.unizar.es<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>http://listas.unizar.es/cgi-bin/mailman/listinfo/fis<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>----------<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>INFORMACIN SOBRE PROTECCIN DE DATOS DE CARCTER
PERSONAL<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Ud. recibe este correo por pertenecer a una lista de
correo gestionada por la Universidad de Zaragoza.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Puede encontrar toda la informacin sobre <st1:City
w:st="on"><st1:place w:st="on">como</st1:place></st1:City> tratamos sus datos
en el siguiente enlace:
https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Recuerde que si est suscrito a una lista voluntaria
Ud. puede darse de baja desde la propia aplicacin en el momento en que lo
desee.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>http://listas.unizar.es<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>----------<o:p></o:p></span></font></p>
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