Physics

"If the same amount of energy is supplied as heat...at a lower temperature... the change in entropy is greater."

"The concept of entropy was... rendered quantitatively precise by Rudolph Clausius in 1856... by defining the change... when energy is transferred to a system as heat. Specifically...Change\;in\;entropy = \frac{energy\;supplied\;as\;heat}{temperature\;at\;which\;the\;transfer\;occurs}[N]ote... temperature... is on the absolute scale..."

"You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage."

"The new information technologies can be seen to drive societies toward increasingly dynamic high-energy regions further and further from thermodynamical equilibrium, characterized by decreasing specific entropy and increasingly dense free-energy flows, accessed and processed by more and more complex social, economic, and political structures."

"After the invention of the steam-engine... by James Watt, the attention of engineers and of scientific men was directed to... its further improvement. ...Sadi Carnot, in 1824, published Réflexions sur la Puissance Motrice du Feu... [which] examined the relations between and the work done by heat used in an ideal engine, and by reducing the problem to its simplest form and avoiding...questions relating to details, he succeeded in establishing the conditions upon which the economical working of all heat-engines depends. ...Though the proof was invalid, the proposition remained true... Carnot's memoir remained for a long time unappreciated, and it was not until use was made of it by William Thomson... in 1848, to establish an absolute scale of temperature, that the merits of the method proposed in it were recognized. ...[H]e found that Carnot's proposition could no longer be proved by denying the possibility of "the ," and was led to lay down a second fundamental principle... now called the Second Law of Thermodynamics. ...It was published in March, 1851. In the previous year Clausias published a discussion of the same question... in which he lays down a principle for use in the demonstration of Carnot’s proposition, which, while not the same in form as Thomson’s, is the same in content, and ranks as another statement of the Second Law of Thermodynamics. Clausius followed up this paper by others, and subsequently published a book in which the subject of Thermodynamics was given a systematic treatment, and in which he introduced and developed the important function called by him the ."

"So if we're going to ask... What is life? ...Erwin Schrödinger wrote a famous book on that theme ...Two famous ideas ...emerged ...one ...was ...that genes are a code-script, and that was the first time anybody had used the word "code-script" or really thought in terms of information, in biology. ...This was before DNA was discovered. He was a direct inspiration to Watson and Crick and many others. The second theme... was how life maintains its organization over time, and why don't we just fall to pieces as entropy would tend to suggest... He talked about life feeding on negative entropy, or "negentropy"... [H]e talked about continually sucking order... from its environment. ...[I]t's a wonderful book. ...[H]e said, "If I had been catering for physicists alone I should have let the discussion turn on free energy instead." ...In more modern terms he's saying something like life is the harnessing of in such a way that the energy-harnessing device makes a copy of itself. ...[H]e's linking the two key themes of biology ...information and energy together."

"It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through . Both of them have sensory receptors as one stage in their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended action, is reported back to the central regulatory apparatus. This complex of behavior is ignored by the average man, and in particular does not play the role that it should in our habitual analysis of society; for just as individual physical responses may be seen from this point of view, so may the organic responses of society itself. I do not mean that the sociologist is unaware of the existence and complex nature of communications in society, but until recently he has tended to overlook the extent to which they are the cement which binds its fabric together."

"There is nothing supernatural about the process of to states of higher entropy; it is a general property of systems, regardless of their materials and origin. It does not violate the Second Law of thermodynamics since the decrease in entropy within an open system is always offset by the increase of entropy in its surroundings."

"But as I was... too much devoted to pure phenomenology to inquire more closely into the relation between entropy and probability, I felt compelled to limit myself to the available experimental results. Now, at that time... 1899, interest was centred on the law of the distribution of energy... proposed by W. Wien... On calculating the relation following from this law between the entropy and energy of a resonator the remarkable result is obtained that the reciprocal value of the above differential coeffcient... R, is proportional to the energy. This extremely simple relation can be regarded as an adequate expression of Wien's law..."

"[M]y previous studies on the second law of thermodynamics served me here... in that my first impulse was to bring not the temperature but the entropy of the resonator into relation with its energy, more accurately not the entropy itself but its second derivative with respect to the energy... [T]his differential coefficient... has a direct physical significance for the irreversibility of the exchange of energy between the resonator and the radiation."

"If energy leaves a body as heat... 'energy supplied as heat' is negative, so the change in entropy is negative... the entropy of the body decreases..."

"Work itself does not generate or reduce entropy."

"The third model regards mind as an information processing system. This is the model of mind subscribed to by cognitive psychologists and also to some extent by the ego psychologists. Since an acquisition of information entails maximization of negative entropy and complexity, this model of mind assumes mind to be an open system."

"I cannot read any significance into a physical world that is held... upside down. For that reason I am interested in entropy not only because it shortens calculations which can be made by other methods, but because it determines an orientation which cannot be found by other methods. ...[T]ime makes a dual entry and thus forms an intermediate link between the internal and the external. This is shadowed partially by the scientific world of primary physics (which excludes time's arrow), but fully when we... include entropy. ...[It] has generally been assumed that the object of the quest is to find out all that really exists. There is another quest... to find out all that really becomes."

"Investigations of the entropy of substances at low temperatures have produced very important information regarding the structure of crystals, the work of Giauque and his collaborators being particularly noteworthy. For example, the observed entropy of crystalline hydrogen shows that even at very low temperatures the molecules of orthohydrogen in the crystal are rotating about as freely as in the gas; ... subsequent to this discovery the phenomenon of rotation of molecules in crystals was found to be not uncommon."

"My colleague Paul Glansdorff and I have investigated the problem as to if the results of near-equilibrium can be extrapolated to those of far - from-equilibrium situations and have arrived at a surprising conclusion: Contrary to what happens at equilibrium, or near equilibrium, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production."

"Whilst the physicist would... say that the matter of this... [dining] table... is really a curvature of space, and its colour is really an electromagnetic wavelength, I do not think that he would say that the familiar moving on of time is really an entropy-gradient. ...[T]here is something as yet ungrasped behind the notion of entropy—some mystic interpretation... not apparent in the definition... [W]e strive to see that entropy-gradient may really be the moving on of time (instead of vice-versa)."

"Use "entropy" and you can never lose a debate, von Neumann told Shannon - because no one really knows what "entropy" is."

"The quality of stored energy is measured by... entropy. ...[T]he lower the entropy the higher the quality."

"Clausius proposed... The entropy of an isolated system increases in any spontaneous change."

"[T]he Kelvin statement is equivalent to... 'your engine will work only if you waste some energy'..."

"In the limiting case, [entropy] stays the same. If it increases.., the process is irreversible. If it remains the same.., the process is reversible... [i.e.,] you can let it run backwards."

"Entropy... was discovered and exalted because it was essential to practical applications of physics... But by it science has been saved from a fatal narrowness. ...[T]here would have been nothing to represent "becoming" in the physical world."

"Entropy was not in the same category as the other physical quantities ...and the extension ...was in a very dangerous direction. ...But entropy had secured a firm place in physics before it was discovered that it was a measure of the random element in arrangement. It was in great favour with the engineers. ...[A]t that time it was the general assumption that the Creation was the work of an engineer (not of a mathematician, as is the fashion nowadays)."

"My greatest concern was what to call it. I thought of calling it 'information,' but the word was overly used, so I decided to call it 'uncertainty.' When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, 'You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.'"

"Prigogine was also concerned with the broader philosophical issues raised by his work. In the 19th century the discovery of the second law of thermodynamics, with its prediction of a relentless movement of the universe toward a state of maximum entropy, generated a pessimistic attitude about nature and science. Prigogine felt that his discovery of self-organizing systems constituted a more optimistic interpretation of the consequences of thermodynamics. In addition, his work led to a new view of the role of time in the physical sciences."

"Kelvin... formed... the view that... the essential component of the steam engine is the cold sink—the surroundings into which waste heat is discarded. The crucial part of the engine... didn't have to be designed or constructed... inverting common sense. ...Kelvin's conceptual somersault led him to promote ...the central ...cold sink to a universal principle ...all viable engines have a cold sink ...not ...[in] those words but ...[in] essence ...Take away the cold sink and the engine stops ..."

"Suppose that we are asked to arrange the following in two categories— distance, mass, electric force, entropy, beauty, melody. [T]here are the strongest grounds for placing entropy alongside beauty and melody... Entropy is only found when the parts are viewed in association... [as are] beauty and melody. All three are features of arrangement. ...The reason why this [entropy] stranger can pass itself off among the aborigines of the physical world is... the language of arithmetic. It has... measure-number... at home in physics."

"[T]he conception associated with entropy... marked a reaction from the view that everything to which science must pay attention is discovered by a microscopic dissection of objects. ...[T]he centre of interest is shifted from the entities reached by the customary analysis (atoms, electric potentials, etc.) to qualities possessed by the system as a whole... The artist... resorts to an impressionist painting. ...[T]he physicist has found ...his impressionist scheme is just as much exact science and even more practical ...than his microscopic scheme."

"Carnot was... wrong about his perception of the steam engine, but... the essence... shone through... his fundamental misconception... that heat is a fluid—caloric—that flows from a hot reservoir [source] to a cold sink... [to] turn an engine... as [does] a waterwheel... by water. ...He ...considered heat ...neither created not destroyed as it flowed ...[H]e was able to prove ...efficiency of an idealized steam engine ...that ignores friction, leaks ...[etc.] is determined only by the temperatures of the ...source and ...sink ...independent of ...pressure and ...working substance [e.g., water, steam or air]. ...[T]he hot reservoir should be as hot as possible and the cold... as cold as possible. All other variables were fundamentally irrelevant."

"All viable engines have a cold sink is one statement of the Second Law of thermodynamics. ...[T]his form of words captures its essence."

"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers: the law of revolution is not a social law, but an immeasurably greater one. It is a cosmic, universal law—like the laws of the and of the dissipation of energy (entropy). Some day, an exact formula for the law of revolution will be established. And in this formula, nations, classes, stars—and books—will be expressed as numerical quantities."

"Because entropy is not really a classical quantity, we must build quantum mechanics into the definition. ... It suffices to define entropy as the logarithm of the number of quantum states accessible to a system."

"[S]uppose that we had to identify force with entropy-gradient. That would only mean that entropy-gradient is a condition which stimulates a nerve, which thereupon transmits an impulse to the brain, out of which the mind weaves its own peculiar impression of force. ...It is absurd to pretend that we are in ignorance of the nature of organisation in the external world in the same way that we are ignorant of the intrinsic nature of potential. It is absurd to pretend that we have no justifiable conception of "becoming"... That dynamical quality... has to do much more than pull the trigger of a nerve. ...a moving on of time is a condition of consciousness. ...It is the innermost Ego of all which is and becomes."

"Consciousness, besides detecting time's arrow, also roughly measures the passage of time. ...but is a bit of a bungler in carrying it out. ...Our consciousness somehow manages to keep ...record of the flight of time ...reading some kind of clock in the material brain ...a better analogy would be an entropy-clock ...primarily for measuring the rate of disorganisation of energy, and only roughly keeping pace with time. ...[I]n forming our ideas of duration and of becoming... [e]ntropy-gradient is... the direct equivalent of the time of consciousness in both... aspects. Duration measured by physical clocks (time-like interval) is only remotely connected."

"Progress imposes not only new possibilities for the future but new restrictions. It seems almost as if progress itself and our fight against the increase of entropy intrinsically must end in the downhill path from which we are trying to escape."

"It had become the regular outlook of science... that constellations are not to be taken seriously, until the constellation of entropy made a solitary exception. When we analyze the picture into a large number of particles of paints, we lose the aesthetic significance of the picture. The particles... go into the scientific inventory, and it is claimed that everything that there really was in the picture is kept. But this way of keeping... may be... losing ... The essence of a picture... is arrangement."

"Nernst's discovery was induced by the fact that even at room temperature entropy plays an astonishingly insignificant role in many chemical reactions."

"Rudolph Clausius... noticed a common feature of nature and had the stature... to publish [in 1850, Über die bewegende Kraft der Wärme (On the motive force of heat)] what others might think a simpleton's observation: heat does not flow from a cooler to a hotter body... [I]n this and subsequent papers he developed this... into a quantitative principle..."

"Paul Davies, The Demon in the Machine (Sep. 7, 2019) 6th International FQXi Conference, "Mind Matters: Intelligence and Agency in the Physical World." A YouTube video source, 4:31."

"The fundamental problem about trying to define life in terms of physics is easily explained. If you go to a physics department... you'll be given a definition in terms of matter... force... energy... entropy... free energy, molecular binding affinities, and so on. If you go to a biology department... you'll be given a very different narrative in terms of... instructions, transcription, , translation, coding, signals... Biologists use information-speak... informational qualities... physicists define life in terms of physical quantities."

"I know of no theorem that tells you... the maximum amount of change that agency can achieve in the universe, and what interests me... is agency at the end of the universe. If you end up in , which has a temperature and a horizon entropy, can you do anything with... those thermal fluctuations? Can you mine them... to extract energy?"

"A natural guess is that... a black hole's entropy is... proportional to its volume. But in the 1970s and Stephen Hawking discovered that this isn't right. Their... analyses showed that the entropy... is proportional to the area of its ... less than what we'd naïvely guess. ...Berkenstein and Hawking found that... each square being one by one Planck length... the black hole's entropy equals the number of such squares that can fit on its surface... each Planck square is a minimal unit of space, and each carries a minimal, single unit of entropy. This suggests that there is nothing, even in principle, that can take place within a Planck square, because any such activity could support disorder and hence the Planck square could contain more than a single unit of entropy... Once again... we are led to the notion of an elemental spatial entity."

"Newton and his theories were a step ahead of the technologies that would define his age. Thermodynamics, the grand theoretical vision of the nineteenth century, operated in the other direction with practice leading theory. The sweeping concepts of energy, , work and entropy, which thermodynamics (and its later form, statistical mechanics) would embrace, began first on the shop floor. Originally the domain of engineers, thermodynamics emerged from their engagement with machines. Only later did this study of heat and its transformation rise to the heights of abstract physics and, finally, to a new cosmological vision."

"The equations of Newtonian mechanics are reversible in time and Poincaré proved that if a mechanical system is in a given state it will return infinitely often to a state arbitrarily close to the given one. Zermelo deduced that the Second Law of Thermodynamics is impossible in a mechanical system. Boltzmann asserted that entropy increases almost always, rather than always. However he believed that Poincaré's result, although correct in theory, was in practice impossible to observe since the time before a system returns to near its original state was too long."

"Black holes have the universe's most inscrutable poker faces. ...When you've seen one black hole with a given mass, charge, and spin (though you've learned these thing indirectly, through their effect on surrounding gas and stars...) you've definitely seen them all. ...black holes contain the highest possible entropy ...a measure of the number of rearrangements of an object's internal constituents that have no effect on its appearance. ...Black holes have a monopoly on maximal disorder. ...As matter takes the plunge across a black hole's ravenous , not only does the black hole's entropy increase, but its size increases as well. ...the amount of entropy ...tells us something about space itself: the maximum entropy that can be crammed into a region of space—any region of space, anywhere, anytime—is equal to the entropy contained within a black hole whose size equals the region in question."

"The homeostatic principle does not apply literally to the functioning of all complex living systems, in that in counteracting entropy they move toward growth and expansion."

"Just like a computer, we must remember things in the order in which entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases. You can’t have a safer bet than that!"

"He sat in the window thinking. Man has a for order. Keys in one pocket, change in another. Mandolins are tuned G D A E. The physical world has a tropism for disorder, entropy. Man against Nature . . . the battle of the centuries. Keys yearn to mix with change. Mandolins strive to get out of tune. Every order has within it the germ of destruction. All order is doomed, yet the battle is worth while."

"If for the entire universe we conceive the same magnitude to be determined, consistently and with due regard to all circumstances, which for a single body I have called entropy, and if at the same time we introduce the other and simpler conception of energy, we may express in the following manner the fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat. 1. The energy of the universe is constant. 2. The entropy of the universe tends to a maximum."