<div dir="ltr"><div>Good morning, FISers</div><div><br></div>What a great theme of discussion, Arieh!<div>Of course, to connect life sciences to "matter" science is not "natural", because we are trained to be specialists. </div><div>Interdisciplinarity and, in this case, Scientific Transposition (as defined in my thesis), can be challenging.</div><div>Your work is amazing and fundamental, especially for non physicists.</div><div>Congratulations!!!<br></div><div><br></div><div>Um abraço!</div><div><br></div><div>Moisés</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Em seg., 4 de jan. de 2021 às 15:05, Arieh Ben-Naim <<a href="mailto:ariehbennaim@gmail.com">ariehbennaim@gmail.com</a>> escreveu:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><br><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>From: <strong class="gmail_sendername" dir="auto">Pedro C. Marijuan</strong> <span dir="auto"><<a href="mailto:pcmarijuan.iacs@aragon.es" target="_blank">pcmarijuan.iacs@aragon.es</a>></span><br>Date: Sat, Jan 2, 2021 at 8:57 PM<br>Subject: Entropy, the Second Law, and Life<br>To: Arieh Ben-Naim <<a href="mailto:ariehbennaim@gmail.com" target="_blank">ariehbennaim@gmail.com</a>><br></div><br><br>
<div>
<p>Dear FIS Discussants,</p>
<p>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 <b>"Entropy:
The greatest Blunder in the History of Science"</b>. 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).</p>
<p>Best wishes</p>
<p>Arieh<br>
</p>
<p>----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------<br>
</p>
<p> </p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:center" align="center"><font size="+3"><b><span lang="EN-US">Entropy, the Second Law,
and Life</span></b></font></p>
<font size="+3"> </font>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:center" align="center"><font size="+3"><b><span lang="EN-US">Arieh Ben-Naim</span></b></font></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:center" align="center"><font size="-1" face="Helvetica, Arial, sans-serif"><i><span style="font-size:11pt;color:black" lang="EN-US">Emeritus Professor,
Department of Physical Chemistry</span></i><i><span style="font-size:11pt;color:black" lang="EN-US">, The Hebrew University of
Jerusalem</span></i></font> </p>
<p><b><font size="+2"> </font></b></p>
<p><u><font size="+2"><b>Introduction</b></font></u><span lang="EN-US"></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">I would like to
start this article with a quotation by Albert Einstein on
thermodynamics:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><b><i><span lang="EN-US">“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.”</span></i></b></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">Most people who use this quotation, emphasize the
last part, namely, that Thermodynamics will “<i>never be
overthrown</i>.” Of course I agree with that part. However, my
emphasis, in this article is on the <i>“</i></span><i><span lang="EN-US">framework
of applicability.” </span></i><span lang="EN-US">My main point is that entropy and the Second Law
were used far <span>beyond
their</span><i> “</i></span><i><span lang="EN-US">framework
of applicability.” </span></i><span lang="EN-US"><span> </span>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].</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">The application
of entropy and the Second Law to a living system is based on two
erroneous assumptions:</span></p>
<p style="margin-bottom:3pt;text-align:justify"><span lang="EN-US"><span>1.<span> </span></span></span><span lang="EN-US">Entropy is a
measure of disorder (or disorganization)</span></p>
<span lang="EN-US"><span><span> </span></span></span><span lang="EN-US">Life is understood
as a process towards organization and creation of order</span>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">From these two
assumptions it follows, almost naturally that life-processes
seem to be “a struggle against the Second Law of
Thermodynamics.”</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">In
this article we shall distinguish between two different
questions:</span><span lang="EN-US"> The first one,
the possibility of <i>defining </i>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!</span> </p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US"> </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><font size="+1"><b><span lang="EN-US"><i>Can
entropy be defined for any living system?</i></span></b></font><font size="+2"><b><span lang="EN-US"> </span></b></font></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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 <i>mental processes</i> 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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">Everyone knows
that life phenomena are the most complex, intricate,
interesting, wonderful, and whatever one wishes to ascribe to
it. During the 20<sup>th</sup> 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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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.<span> </span></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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 (CO<sub>2</sub>)
and water (H<sub>2</sub>O) to high energy sugars.<span> </span>In all of these cases the
reactions could be studied <i>in vitro</i>, i.e. in a
laboratory setting, or in test tubes, isolated from the entire
complicated environment in the cell (<i>in vivo</i>).</span><span lang="EN-US"> Clearly,
thermodynamics was, and still is, the main tool in understanding
the energetics of these reactions.</span><span lang="EN-US"><br>
</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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.</span><span lang="EN-US"> 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.</span>
</p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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 <i>state function.</i> This means that entropy is
definable for a well-defined <i>thermodynamic system</i> at
equilibrium.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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 <i>physical state</i> of the
body, there is still the question of how to describe the <i>state
of the mind</i> of the person? The last question brings us to
the classical question about the nature of the mind.</span><span lang="EN-US"> 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 <i>hypothesis</i>,
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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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]. <br>
</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US"> </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><u><font size="+2"><b>The history of application of Entropy and the
Second Law to living systems</b></font></u></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">Perhaps the
oldest association of Second Law with life is due to Boltzmann.
On May 29, 1886, </span><span lang="EN-US"><a href="http://www.eoht.info/page/Ludwig+Boltzmann" target="_blank"><span>Ludwig
Boltzmann</span></a></span><span lang="EN-US"> presented a talk
at the Festive Session of the Imperial Academy of Sciences in
Vienna where he discussed “<b><i>The S</i></b></span><span lang="EN-US"><a href="http://www.eoht.info/page/second+law" target="_blank"><b><i><span>econd Law</span></i></b></a></span><b><i><span lang="EN-US"> of
Thermodynamics”</span></i></b><span lang="EN-US"> with special
emphasis on its application in relation to </span><span lang="EN-US"><a href="http://www.eoht.info/page/Charles+Darwin" target="_blank"><span>Charles
Darwin</span></a></span><span lang="EN-US">'s 1859 theory
of </span><span lang="EN-US"><a href="http://www.eoht.info/page/evolution" target="_blank"><span>evolution</span></a></span><span><span lang="EN-US"> [16]</span></span><span lang="EN-US">.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">The most-</span><span lang="EN-US"><a href="http://www.eoht.info/page/Entropy+quotes" target="_blank"><span>quoted</span></a></span><span lang="EN-US"> passage from
this lecture is that </span><span lang="EN-US"><a href="http://www.eoht.info/page/life" target="_blank"><span>life</span></a></span><span lang="EN-US"> is a <b>struggle
for </b></span><span lang="EN-US"><a href="http://www.eoht.info/page/Entropy" target="_blank"><b><span>entropy</span></b></a></span><span lang="EN-US">: </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">“<i>The general </i></span><span lang="EN-US"><a href="http://www.eoht.info/page/Struggle+for+existence" target="_blank"><i><span>struggle for existence</span></i></a></span><i><span lang="EN-US"> of </span></i><span lang="EN-US"><a href="http://www.eoht.info/page/Animate" target="_blank"><i><span>animate</span></i></a></span><i><span lang="EN-US"> </span></i><span lang="EN-US"><a href="http://www.eoht.info/page/Being" target="_blank"><i><span>beings</span></i></a></span><i><span lang="EN-US"> is not </span></i><span lang="EN-US"><a href="http://www.eoht.info/page/struggle" target="_blank"><i><span>struggle</span></i></a></span><i><span lang="EN-US"> for raw </span></i><span lang="EN-US"><a href="http://www.eoht.info/page/Matter" target="_blank"><i><span>materials</span></i></a></span><span><i><span lang="EN-US">, </span></i></span><i><span lang="EN-US">these,
for organisms, are air, water and soil, all abundantly
available, nor for </span></i><span lang="EN-US"><a href="http://www.eoht.info/page/Energy" target="_blank"><i><span>energy</span></i></a></span><i><span lang="EN-US">, which exists
in plenty in anybody in the form of </span></i><span lang="EN-US"><a href="http://www.eoht.info/page/Heat" target="_blank"><i><span>heat</span></i></a></span><i><span lang="EN-US"> Q, but of <b>a </b></span></i><span lang="EN-US"><a href="http://www.eoht.info/page/Struggle+for+entropy" target="_blank"><b><i><span>struggle for entropy</span></i></b></a></span><i><span lang="EN-US">, which becomes available
through the transition of energy from the hot sun to the cold
earth.” </span></i><span lang="EN-US"></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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 </span><span lang="EN-US"><a href="http://www.eoht.info/page/life" target="_blank"><span>life</span></a></span><span lang="EN-US"> is a “<b>struggle
for </b></span><span lang="EN-US"><a href="http://www.eoht.info/page/Entropy" target="_blank"><b><span>entropy</span></b></a></span><span><b><span lang="EN-US">”</span></b></span><span lang="EN-US"></span></p>
<span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">However, the
most influential physicist who propagated the erroneous ideas
about entropy and life was Erwin </span><span lang="EN">Schrödinger.</span><span lang="EN"> I</span><span lang="EN-US">n 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.<span></span></span></p>
</span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><font size="+1"><i><b><span lang="EN">Schrödinger’s book: What is life?</span></b></i></font></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">On the
question: “What is life? one cannot avoid starting with the
most famous book written by Schrödinger [3].</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">This book
is based on lectures delivered by Schrödinger in Dublin 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].</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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:</span></p>
</span><span lang="EN-US"></span><span lang="EN-US"> </span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN">“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?”</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">His
preliminary answer to this question:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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</i>.”</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">On page
10 Schrödinger provides some hints about his intention to use
the Second Law:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">My
impression is that Schrödinger used the terms “<i>orderly
thing,” “orderliness,” “physical organization,” “well
ordered organization,” </i>and similar terms in
anticipation of his usage of entropy and the Second Law of
thermodynamics in later chapters.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.”</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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: </span></p>
</span><span lang="EN-US"></span><span lang="EN-US"> </span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN">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.</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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 <i>meaningless</i>;
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.</span></p>
</span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>The general principle
involved is the famous Second Law of Thermodynamics (entropy
principle) and its equally famous statistical foundation.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">His main
claim is that “living matter evades the decay to equilibrium.”</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">Then he
asks:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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 </i><b><i>metabolism</i>.”</b></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">I believe
that the book’s highlight is reflected on page 76:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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 <i>negative entropy</i> 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.</span></p>
</span><span lang="EN-US"></span><span lang="EN-US"> </span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US"></span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">Did Schrödinger
have a bad slip of the tongue in this statement? It seems to
me that Schr</span><span lang="EN">ö</span><span lang="EN">dinger
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.”</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN">“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.”</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.</span></p>
</span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.</span></p>
</span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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].</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN">“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.”</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">I fully
agree!</span><span lang="EN"></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">Likewise,
Perutz had a similar criticism of Schrodinger’s book, in 1987)
[18]:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN-US">“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.”</span></i></p>
</span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.</span></p>
</span><span lang="EN-US"></span><span lang="EN-US">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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 “<i>complete theory of
life</i>” 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. <br>
</span></p>
</span>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"> </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><u><font size="+2"><b><span lang="EN">More on Entropy, the Second Law and life</span></b></font></u></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">Combining these
two erroneous views inevitably leads us to the association of
life phenomena with a <i>decrease</i> 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 <i>cannot be defined
forany living system</i>, and the Second Law, in its entropy
formulation does not apply to living systems.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">Here is an
example from Katchalsky[19] in (1963):</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">Volkenstein [20],
comments on the “anti-entropic” by saying:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN-US">“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…”</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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.”<span> </span></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">Here is
another outstanding example:</span></p>
<span lang="EN">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">In
Atkins’ (1984) introduction to his book [11] he writes:</span></p>
</span><span lang="EN"></span><span lang="EN">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>In Chapter 8 we also
saw how the Second Law accounts for the emergence of the
intricately ordered forms characteristic of life.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN">“We
shall see how chaos can run apparently against Nature, and
achieve that most unnatural of ends, life itself.”</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">Finally,
after discussing some aspects of processes in a living
organism, Atkins concludes his book:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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.</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN">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.”</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">So beautiful and so empty combination of words!</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><font size="+1"><i><b><span lang="EN">Do we feed on negative entropy?</span></b></i></font></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">Brillouin
[21], “<i>feeding on the negative entropy</i>” ideas
pronounced by Schrödinger, goes even further and claims that:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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.”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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 <i>negentropy</i>!</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">While I
am still baffled with the concept of <i>negative entropy</i>, or
its shorter version <i>negentropy</i>,
I was greatly relieved to read Hoffmann’s [22] explanation:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"><span> </span>“<i>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).”</i></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">In more
modern books the meaningless notion of negative entropy (or
neg-entropy) is replaced by the more meaningful term of <i>low entropy</i>.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">Is it
meaningful to claim that we, living organisms feed on low
entropy food?</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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 <i>state</i> of
a living system. </span></p>
</span><span lang="EN"></span><span lang="EN"></span><span lang="EN"></span><span lang="EN"></span><span lang="EN">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:center" align="center"><span lang="EN-US">“IT IS ENTROPY,
NOT ENERGY THAT DRIVES THE WORLD”</span></p>
</span><span lang="EN"></span><span lang="EN"></span><span lang="EN"></span><span lang="EN"></span><span lang="EN"></span><span lang="EN">
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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. </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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:</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><i><span lang="EN-US">“If all we
needed was energy rather than entropy, we would head for the
heat of the Sahara rather than toward our meal.”</span></i></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">First, I think
it is unfair (to say the least) to say “if all we <i>needed</i>
was energy.” No one needs <i>only</i> 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
Sahara. </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">This comment is
dangerous because the energy that we need is energy stored in
some chemical compounds, not the “heat of the Sahara.” If one
were to believe that energy is important (and assuming that
all other things including water, are available) then going to
the Sahara instead of having the next meal, will kill you, so
better not to heed the Rovelli’s advice.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">If you
swallow a cube of ice at 0</span><span lang="EN-US"> </span><span lang="EN">, or
drink the equivalent amount of liquid water at 0</span><span lang="EN-US"> </span><span lang="EN">, 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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">To conclude
this section, it should be stressed that my objection to the
usage of entropy and the Second Law applies to the <i>entire</i>
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. </span></p>
</span>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"> </p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><font size="+2"><b><u>Some concluding remarks on Entropy, the Second
Law and Life</u></b></font></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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 <i>entropy</i>, or of the
Second Law to a living system.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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 <i>information</i> 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 <i>tends</i> to an equilibrium
state, and whether it will ever reach an equilibrium state.
Therefore, as long as a living system is <i>alive</i>, 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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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. </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN">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.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN"> </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><font size="+2"><b><span lang="EN-US">References</span></b></font></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">1. Ben-Naim, A.
(2016), <i>Entropy the Truth the Whole Truth and Nothing but
the Truth</i>, World Scientific Publishing, Singapore </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">2.<span> </span>Ben-Naim, A. (2020), <i>The
Greatest Blunder in the History of Science, involving Entropy,
Time, Life and the Universe. </i>Independently Publisher,
Amazon.<span> </span></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">3.</span><span lang="EN-US"><span>
Schrödinger (1944), <i>What Is Life? : The Physical Aspect of
the Living Cell,</i></span></span><span lang="EN-US"> Based on
lectures delivered under the auspices of the Dublin Institute
for Advanced Studies at Trinity College, Dublin, in February
1943</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">4. Penrose, R.
(1989),<i> The Emperor’s Mind. Concerning Computers, Minds and
the Law of Physics, </i>Penguin Books, New York</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">5. Penrose, R.
(1994)</span><span lang="EN">Penrose, R.
(1994), <i>Shadows of the
Mind: An Approach to the Missing Science of Consciousness</i>,
Oxford University Press, Oxford</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">6. Crick, F.
(1994), “<i>The Astonishing
Hypothesis</i>,” The Scientific Search For the Soul,”
Touchstone, Simon and Shuster, New York</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">7. Dennett, D.
(2017), “<i>From Bacteria to
Bach and Back</i>,” The Evolution of Minds,” W. W. Norton,
Inc. USA, Henry Holt and Co., New York (2018)</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">8. Ben-Naim, A.
(2017), <i>The Four Laws that do not drive the Universe</i>,
World Scientific Publishing, Singapore</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">9. Ben-Naim A.
and Casadei D. (2017<i>), Modern Thermodynamics</i>, World
Scientific Publishing, Singapore</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">10. Ben-Naim, A.
(2018), <i>Time’s Arrow</i>?<i>The Timeless Nature of Entropy
and the Second Law of Thermodynamics.</i> Lulu Publishing
Services</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">11. Atkins, P.
(1984),<i>The Second Law</i>, Scientific American Books, W. H.
Freeman and Co., New York</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">12.<span> </span>Atkins, P. (2007), <i>Four Laws That Drive The
Universe</i>, Oxford University Press</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">13. Brush, S. G.
(1976), <i>The Kind of Motion We Call Heat. A History of the
Kinetic Theory of Gases in The 19<sup>th</sup> Century</i>, <i>Book
2: Statistical Physics and Irreversible Processes</i>.
North-Holland Publishing Company</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">14. Brush, S. G.
(1983), <i>Statistical Physics and the Atomic Theory of Matter,
from Boyle and Newton to Landau and Onsager</i>. Princeton
University Press, Princeton.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">15. Ben-Naim, A. (2020),<i>Time for Everyone and
Time for Everything</i>, Independent<span> </span>Publisher, Amazon <span style="color:black"></span></span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">16. Boltzmann, L.
(1877), <i>Vienna Academy</i>. <b>42</b>, <i>“Gesammelte
Werke”</i> p. 193.</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">17. Hager, T.
(1995),<i> Forces of Nature, the Life of Linus Pauling, </i>Simon
and Schuster, New York </span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">18. Perutz, M.F.
(1987),<i>Physics and the riddle of life</i>, </span><span lang="EN-US"><a href="https://www.nature.com/nature" target="_blank"><i><span>Nature</span></i></a></span><span lang="EN-US">, <b> 326</b>, 555–558</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">19. Katchalsky,
A. (1963), <i>Nonequilibrium Thermodynamics</i>, Int. Sci.
Technol, 43</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">20. Volkenstein,
M. V. (2009), <i>Entropy and Information</i>, translated by A.
Shenitzer and A. G. Burns, Birkhauser, Berlin</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">21<i>. </i>Brillouin,
L. (1962), <i>Science and Information Theory</i>, Academic
Press, New York</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">22. Hoffman, P.M.
(2012), <i>Life’s Ratchet,
How Molecular Machines Extract Order from Chaos</i>, Basic
Books, New York</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">23. Rovelli, C.
(2018) <i>The Order of Time, </i>Riverhead books, New York</span></p>
<p class="MsoNormal" style="margin-bottom:3pt;text-align:justify"><span lang="EN-US">24. </span><span lang="EN">Styer, D.F. (2008), <i>Entropy
and Evolution</i>, Am. Journal of Physics, 76, 1031</span><span lang="EN-US"></span></p>
<p class="MsoNormal" style="margin-bottom:3pt"><span style="color:black" lang="EN-US">25.</span><span lang="EN"> Sanford,
J. C. (2005), <i>Genetic
Entropy and the Mystery of the Genome</i>, Ivan Press, a
division of Elim Publishin</span></p>
<p class="MsoNormal" style="margin-bottom:3pt"><span style="color:black" lang="EN-US"> </span></p>
<pre cols="72">--
-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
<a href="mailto:pcmarijuan.iacs@aragon.es" target="_blank">pcmarijuan.iacs@aragon.es</a>
<a href="http://sites.google.com/site/pedrocmarijuan/" target="_blank">http://sites.google.com/site/pedrocmarijuan/</a>
------------------------------------------------- </pre>
</div>
</div><br clear="all"><div><br></div>-- <br><div dir="ltr">Prof. Arieh Ben-Naim<br>Department of Physical Chemistry<br>The Hebrew University of Jerusalem<br>Jerusalem, 91904<br>Israel</div></div>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div><div dir="ltr">Moisés André Nisenbaum</div><div>Coordenador do Curso Técnico em Manutenção e Suporte em Informática (MSI)</div><div dir="ltr">Instituto Federal do Rio de Janeiro - IFRJ<br>Campus Rio de Janeiro<br><a href="mailto:moises.nisenbaum@ifrj.edu.br" target="_blank">moises.nisenbaum@ifrj.edu.br</a></div></div><div><br></div><div><div></div><div>Currículo Lattes: <a href="http://lattes.cnpq.br/7720722027872922" target="_blank">http://lattes.cnpq.br/7720722027872922</a> <br></div><div><a href="http://youtube.com/moisesandre" target="_blank">youtube.com/moisesandre</a></div><div><a href="http://facebook.com/moisesandre" target="_blank">facebook.com/moisesandre</a></div><div><a href="http://www.linkedin.com/in/moisesandre" target="_blank">www.linkedin.com/in/moisesandre</a><br></div><div><a href="http://dicas.moisesandre.com.br/" target="_blank">dicas.moisesandre.com.br<br></a></div></div></div></div></div></div></div></div></div></div></div></div>