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

Mon Jan 4 20:47:37 CET 2021

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:
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>  “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:
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>  “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.”
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>  “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:
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>  “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:
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>  “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.”
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> “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.”
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> 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.
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> 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.
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> 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].
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> “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]:
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> “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.
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> 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.
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> More on Entropy, the Second Law and life
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> 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.
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> 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):
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>  “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.”
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> 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.
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> Volkenstein [20], comments on the “anti-entropic” by saying:
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> “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…”
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> 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.”
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> Here is another outstanding example:
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> In Atkins’ (1984) introduction to his book [11] he writes:
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>  “In Chapter 8 we also saw how the Second Law accounts for the emergence of the intricately ordered forms characteristic of life.”
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> 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:
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> “We shall see how chaos can run apparently against Nature, and achieve that most unnatural of ends, life itself.”
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> Finally, after discussing some aspects of processes in a living organism, Atkins concludes his book:
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>  “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.
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> 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.”
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> So beautiful and so empty combination of words!
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> Do we feed on negative entropy?
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> Brillouin [21], “feeding on the negative entropy” ideas pronounced by Schrödinger, goes even further and claims that:
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>  “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!
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> 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:
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>  “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).”
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> In more modern books the meaningless notion of negative entropy (or neg-entropy) is replaced by the more meaningful term of low entropy.
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> Is it meaningful to claim that we, living organisms feed on low entropy food?
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> 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:
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> “IT IS ENTROPY, NOT ENERGY THAT DRIVES THE WORLD”
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> 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.
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> 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.”
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> 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.
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> 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
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> 1. Ben-Naim, A. (2016), Entropy the Truth the Whole Truth and Nothing but the Truth, World Scientific Publishing, Singapore
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> 2.  Ben-Naim, A. (2020), The Greatest Blunder in the History of Science, involving Entropy, Time, Life and the Universe. Independently Publisher, Amazon.
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> 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
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> 4. Penrose, R. (1989), The Emperor’s Mind. Concerning Computers, Minds and the Law of Physics, Penguin Books, New York
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> 5. Penrose, R. (1994)Penrose, R. (1994), Shadows of the Mind: An Approach to the Missing Science of Consciousness, Oxford University Press, Oxford
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> 6. Crick, F. (1994), “The Astonishing Hypothesis,” The Scientific Search For the Soul,” Touchstone, Simon and Shuster, New York
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> 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)
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> 8. Ben-Naim, A. (2017), The Four Laws that do not drive the Universe, World Scientific Publishing, Singapore
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> 9. Ben-Naim A. and Casadei D. (2017), Modern Thermodynamics, World Scientific Publishing, Singapore
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> 10. Ben-Naim, A. (2018), Time’s Arrow?The Timeless Nature of Entropy and the Second Law of Thermodynamics. Lulu Publishing Services
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> 11. Atkins, P. (1984),The Second Law, Scientific American Books, W. H. Freeman and Co., New York
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> 12.  Atkins, P. (2007), Four Laws That Drive The Universe, Oxford University Press
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> 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
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> 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.
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> 15. Ben-Naim, A. (2020),Time for Everyone and Time for Everything, Independent      Publisher, Amazon
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> 16. Boltzmann, L. (1877), Vienna Academy. 42, “Gesammelte Werke” p. 193.
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> 17. Hager, T. (1995), Forces of Nature, the Life of Linus Pauling, Simon and Schuster, New York
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> 18. Perutz, M.F. (1987),Physics and the riddle of life, Nature,  326, 555–558
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> 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
> _______________________________________________
> Fis mailing list
> Fis at listas.unizar.es
> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
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