[Fis] Fwd: Entropy, the Second Law, and Life

Arieh Ben-Naim ariehbennaim at gmail.com
Tue Jan 5 13:13:30 CET 2021

Dear Michel, and whoever interested,

I fully agree that there is no definition of order for a thermodynamic
However, even if there was a definition it will not be relevant to entropy
(except for on “definition” by Callen, who “defines” disorder by Shannon
measure of information.
I have criticized this “definition” in several of my books, specifically in
Entropy: The Greatest Blunder in the History of Science).

In addition, and independently of the availability of a definition to
order, or disorder, I do not think one can apply the concept of Entropy, or
the Second Law to living organisms
Best wishes and a happy new year.

On Mon, Jan 4, 2021 at 21:47 Michel Petitjean <petitjean.chiral at gmail.com>

> Dear Arieh,
> Many thanks for your great contribution.
> Eisnstein was right, the framework of applicability is the main point.
> And it is often neglecetd, about the universe, and about life.
> We can find in many books about thermodynamics a definition of entropy.
> I don't discuss it, even if there is much to say about it.
> An important point is, what is disorder?
> Does anybody can show me a definition of disorder?
> May be the negation of order.
> But what is order ?
> Not the mathematical definition in set theory (partial order, total
> order), it seems to be something else.
> Does anybody can show me a definition of order?
> If somebody can tell me what is order or what is disorder
> (microstates? randomness? else?), my next question follows.
> Is it possible to define what is the maximal order (or minimal
> disorder), and conversely, what is the minimal order (or maximal
> disorder)?
> Once we get clear concepts in simple situations, we may discuss their
> application to life.
> If the concepts are unclear in simple situations, disussing their
> application to life will never end.
> Best regards,
> Michel.
> Michel Petitjean
> Université de Paris, BFA, CNRS UMR 8251, INSERM ERL U1133, F-75013 Paris,
> France
> Phone: +331 5727 8434; Fax: +331 5727 8372
> E-mail: petitjean.chiral at gmail.com (preferred),
>         michel.petitjean at univ-paris-diderot.fr
> http://petitjeanmichel.free.fr/itoweb.petitjean.html
> Le lun. 4 janv. 2021 à 19:03, Arieh Ben-Naim <ariehbennaim at gmail.com> a
> écrit :
> >
> >
> >
> > ---------- Forwarded message ---------
> > From: Pedro C. Marijuan <pcmarijuan.iacs at aragon.es>
> > Date: Sat, Jan 2, 2021 at 8:57 PM
> > Subject: Entropy, the Second Law, and Life
> > To: Arieh Ben-Naim <ariehbennaim at gmail.com>
> >
> >
> > Dear FIS Discussants,
> >
> > 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).
> >
> > Best wishes
> >
> > Arieh
> >
> >
> ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
> >
> > Entropy, the Second Law, and Life
> >
> > Arieh Ben-Naim
> >
> > Emeritus Professor, Department of Physical Chemistry, The Hebrew
> University of Jerusalem
> >
> >
> >
> > Introduction
> >
> > I would like to start this article with a quotation by Albert Einstein
> on thermodynamics:
> >
> > “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.”
> >
> > 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].
> >
> > The application of entropy and the Second Law to a living system is
> based on two erroneous assumptions:
> >
> > 1.   Entropy is a measure of disorder (or disorganization)
> >
> > Life is understood as a process towards organization and creation of
> order
> >
> > From these two assumptions it follows, almost naturally that
> life-processes seem to be “a struggle against the Second Law of
> Thermodynamics.”
> >
> > 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!
> >
> > Can entropy be defined for any living system?
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > 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].
> >
> > The history of application of Entropy and the Second Law to living
> systems
> >
> > 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 Vienna 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].
> >
> > The most-quoted passage from this lecture is that life is a struggle for
> entropy:
> >
> > “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.”
> >
> > 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”
> >
> > 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.
> >
> > Schrödinger’s book: What is life?
> >
> > On the question: “What is life? one cannot avoid starting with the most
> famous book written by Schrödinger [3].
> >
> > 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].
> >
> > 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:
> >
> > “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?”
> >
> > His preliminary answer to this question:
> >
> >  “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.”
> >
> > 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.
> >
> > On page 10 Schrödinger provides some hints about his intention to use
> the Second Law:
> >
> >  “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.”
> >
> > 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.
> >
> > 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.”
> >
> >  “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.”
> >
> > 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:
> >
> > 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.
> >
> > 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.
> >
> >  “The general principle involved is the famous Second Law of
> Thermodynamics (entropy principle) and its equally famous statistical
> foundation.”
> >
> > His main claim is that “living matter evades the decay to equilibrium.”
> >
> >  “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.”
> >
> > Then he asks:
> >
> >  “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.”
> >
> > I believe that the book’s highlight is reflected on page 76:
> >
> >  “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.”
> >
> > 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.
> >
> > 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.”
> >
> > “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.”
> >
> > 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.
> >
> > 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.
> >
> > 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].
> >
> > “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.”
> >
> > I fully agree!
> >
> > Likewise, Perutz had a similar criticism of Schrodinger’s book, in 1987)
> [18]:
> >
> > “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.”
> >
> > 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.
> >
> > 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.
> >
> > More on Entropy, the Second Law and life
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > Here is an example from Katchalsky[19] in (1963):
> >
> >  “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.”
> >
> > 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.
> >
> > Volkenstein [20], comments on the “anti-entropic” by saying:
> >
> > “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…”
> >
> > 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.”
> >
> > Here is another outstanding example:
> >
> > In Atkins’ (1984) introduction to his book [11] he writes:
> >
> >  “In Chapter 8 we also saw how the Second Law accounts for the emergence
> of the intricately ordered forms characteristic of life.”
> >
> > 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:
> >
> > “We shall see how chaos can run apparently against Nature, and achieve
> that most unnatural of ends, life itself.”
> >
> > Finally, after discussing some aspects of processes in a living
> organism, Atkins concludes his book:
> >
> >  “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.
> >
> > 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.”
> >
> > So beautiful and so empty combination of words!
> >
> > Do we feed on negative entropy?
> >
> > Brillouin [21], “feeding on the negative entropy” ideas pronounced by
> Schrödinger, goes even further and claims that:
> >
> >  “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.”
> >
> > 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!
> >
> > 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:
> >
> >  “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).”
> >
> > In more modern books the meaningless notion of negative entropy (or
> neg-entropy) is replaced by the more meaningful term of low entropy.
> >
> > Is it meaningful to claim that we, living organisms feed on low entropy
> food?
> >
> > 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.
> >
> > 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:
> >
> >
> > 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.
> >
> > 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:
> >
> > “If all we needed was energy rather than entropy, we would head for the
> heat of the Sahara rather than toward our meal.”
> >
> > 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 Sahara.
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > Some concluding remarks on Entropy, the Second Law and Life
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> > 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.
> >
> >
> >
> > References
> >
> > 1. Ben-Naim, A. (2016), Entropy the Truth the Whole Truth and Nothing
> but the Truth, World Scientific Publishing, Singapore
> >
> > 2.  Ben-Naim, A. (2020), The Greatest Blunder in the History of Science,
> involving Entropy, Time, Life and the Universe. Independently Publisher,
> Amazon.
> >
> > 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
> >
> > 4. Penrose, R. (1989), The Emperor’s Mind. Concerning Computers, Minds
> and the Law of Physics, Penguin Books, New York
> >
> > 5. Penrose, R. (1994)Penrose, R. (1994), Shadows of the Mind: An
> Approach to the Missing Science of Consciousness, Oxford University Press,
> Oxford
> >
> > 6. Crick, F. (1994), “The Astonishing Hypothesis,” The Scientific Search
> For the Soul,” Touchstone, Simon and Shuster, New York
> >
> > 7. Dennett, D. (2017), “From Bacteria to Bach and Back,” The Evolution
> of Minds,” W. W. Norton, Inc. USA, Henry Holt and Co., New York (2018)
> >
> > 8. Ben-Naim, A. (2017), The Four Laws that do not drive the Universe,
> World Scientific Publishing, Singapore
> >
> > 9. Ben-Naim A. and Casadei D. (2017), Modern Thermodynamics, World
> Scientific Publishing, Singapore
> >
> > 10. Ben-Naim, A. (2018), Time’s Arrow?The Timeless Nature of Entropy and
> the Second Law of Thermodynamics. Lulu Publishing Services
> >
> > 11. Atkins, P. (1984),The Second Law, Scientific American Books, W. H.
> Freeman and Co., New York
> >
> > 12.  Atkins, P. (2007), Four Laws That Drive The Universe, Oxford
> University Press
> >
> > 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
> >
> > 14. Brush, S. G. (1983), Statistical Physics and the Atomic Theory of
> Matter, from Boyle and Newton to Landau and Onsager. Princeton University
> Press, Princeton.
> >
> > 15. Ben-Naim, A. (2020),Time for Everyone and Time for Everything,
> Independent      Publisher, Amazon
> >
> > 16. Boltzmann, L. (1877), Vienna Academy. 42, “Gesammelte Werke” p. 193.
> >
> > 17. Hager, T. (1995), Forces of Nature, the Life of Linus Pauling, Simon
> and Schuster, New York
> >
> > 18. Perutz, M.F. (1987),Physics and the riddle of life, Nature,  326,
> 555–558
> >
> > 19. Katchalsky, A. (1963), Nonequilibrium Thermodynamics, Int. Sci.
> Technol, 43
> >
> > 20. Volkenstein, M. V. (2009), Entropy and Information, translated by A.
> Shenitzer and A. G. Burns, Birkhauser, Berlin
> >
> > 21. Brillouin, L. (1962), Science and Information Theory, Academic
> Press, New York
> >
> > 22. Hoffman, P.M. (2012), Life’s Ratchet, How Molecular Machines Extract
> Order from Chaos, Basic Books, New York
> >
> > 23. Rovelli, C. (2018) The Order of Time, Riverhead books, New York
> >
> > 24. Styer, D.F. (2008), Entropy and Evolution, Am. Journal of Physics,
> 76, 1031
> >
> > 25. Sanford, J. C. (2005), Genetic Entropy and the Mystery of the
> Genome, Ivan Press, a division of Elim Publishin
> >
> >
> >
> > --
> > -------------------------------------------------
> > Pedro C. Marijuán
> > Grupo de Bioinformación / Bioinformation Group
> >
> > pcmarijuan.iacs at aragon.es
> > http://sites.google.com/site/pedrocmarijuan/
> > -------------------------------------------------
> >
> >
> >
> > --
> > Prof. Arieh Ben-Naim
> > Department of Physical Chemistry
> > The Hebrew University of Jerusalem
> > Jerusalem, 91904
> > Israel
> > _______________________________________________
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> > ----------
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> > ----------
Prof. Arieh Ben-Naim
Department of Physical Chemistry
The Hebrew University of Jerusalem
Jerusalem, 91904
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