Energy

"The remarks on negative entropy have met with doubt and opposition from physicist colleagues. ...[I]f I had been catering for them alone I should have let the discussion turn on free energy instead. It is the more familiar notion... [b]ut seemed linguistically too near energy for... the average reader... the concept is a rather intricate one, whose relation to Boltzmann's order-disorder principle is less easy to trace... '[E]ntropy with a negative sign'... is not my invention. It... [is] precisely the thing on which Boltzmann's original argument turned."

"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."

"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."

"I am standing on the threshold about to enter a room. ...I must make sure of landing on a plank travelling twenty miles a second around the sun—a fraction of a second too early or too late, the plank would be miles away. I must do this whilst hanging from a round planet head outward into space, and with a wind of aether... I ought really to look at the problem four-dimensionally as concerning the intersection of my world-line with that of the plank. Then again it is necessary to determine in which direction the entropy of the world is increasing in order to make sure that my passage over the threshold is an entrance, not an exit. Verily, it is easier for a camel to pass through the eye of a needle than for a scientific man to pass through a door. And whether... barn... or church door it might be wiser that he should consent to be an ordinary man... rather than wait til all the difficulties in... scientific ingress are resolved."

"Energy remains constant and entropy always grows and can never be reduced... the essence of the second law of thermodynamics... [i.e.,] the entropy of a system of bodies can... only increase."

"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."

"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."

"When is a piece of matter said to be alive? When it goes on... moving, exchanging material with its environment... When a system... is not alive... all motion usually comes to a standstill... as a result of friction... [T]he whole system fades away into a dead, inert lump of matter. A permanent state is reached, in which no observable events occur. The physicist calls this the state of thermodynamic equilibrium, or of 'maxiumum entropy'."

"[T]he statistical concept of order and disorder... was revealed by... Boltzmann and Gibbs... This too is an exact quantitative connection...entropy = k\log Dwhere k is the... and D is... the atomistic disorder of the body... The disorder... is partly... heat of motion, partly... atoms and molecules being mixed at random... e.g., sugar and water molecules... The gradual 'spreading out' of the sugar over all the water... increases the disorder D, and hence (since the logarithm of D increases with D) the entropy. ...[A]ny supply of heat increases the turmoil of heat motion, that is ...increases D... [W]hen you melt a crystal... you... destroy the neat and permanent arrangement of... atoms or molecules and turn the crystal lattice into a continually changing random distribution."

"If D is a measure of disorder... 1/D... can be regarded as a... measure of order. Since the logarithm of 1/D is... minus the logarithm of D...-(entropy) = k\log 1/D"

"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."

"[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."

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

"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."

"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)."

"The discrimination between cause and effect depends on time's arrow and can only be settled by reference to entropy."

"The more closely we examine the association of entropy with "becoming" the greater do the obstacles appear. If entropy were one of the elementary indefinables of physics there would be no difficulty. Or if the moving on of time were something of which we were made aware through our sense organs there would be no difficulty. ...Suppose that we had to identify "becoming" with an electrical potential-gradient ...through the readings of a voltmeter."

"[T]he law does not prohibit the transfer of heat from cold to hot... [T]o achieve , we have to do work... Clausius's... process... refers to 'natural' or 'spontaneous' changes ...without ...[being] driven by an external agency."

"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)."

"[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."

"Work itself does not generate or reduce entropy."

"Is the random element... the only feature of the physical world which can furnish time with an arrow? ...Nothing in the statistics of an assemblage can distinguish a direction of time when entropy fails to distinguish one. ...[T]his law was only discovered in the last few years ...It is accepted as fundamental in ...atoms and radiation and had proved to be one of the most powerful weapons of progress in such researches. It does not seem to be... deducible from the second law..."

"Except for action and entropy (which belongs to an entirely different class of physical conceptions) all the quantities prominent in pre-relativity physics refer to the three-dimensional sections which are different for different observers."

"Energy is needed to replace not only the mechanical energy of our bodily exertions, but also the heat we continually give off... And that we give off heat is not accidental, but essential. For this is precisely the manner in which we dispose of the surplus entropy we continually produce in our... life process."

"Clausius... summarized... the First and Second Laws: ...[T]he energy of the world is constant; the entropy strives towards a maximum."

"'[E]nergy supplied as heat' appears in the numerator of Clausius' expression, for the greater the energy... as heat, the greater... increase in disorder and therefore... entropy. The... temperature in the denominator fits... this analogy too... for a given supply of heat... [added to] a cool [little thermal motion] object... will introduce a... [relatively large] disturbance, corresponding to a big rise in entropy... [and the same heat added to a] hot [lots of thermal motion] object has relatively little effect, and the increase in entropy is small."

"Entropy, according to Boltzmann, is a measure of a physical probability, and the meaning of the second law of thermodynamics is that the more probable a state is, the more frequently will it occur in nature."

"I was... occupied with the task of giving it a real physical meaning, and this... led me, along Boltzmann's line... to the consideration of the relation between entropy and probability... after some weeks of the most intense work of my life clearness began to dawn... and an unexpected view revealed itself..."

"[W]hat one measures are only the differences of entropy, and never entropy itself, and consequently one cannot speak... of the absolute entropy of a state. But nevertheless the introduction of an appropriately defined absolute magnitude of entropy is... recommended... by its help certain general laws can be formulated with great simplicity."

"[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."

"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."

"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..."

"The significant part played in the origin of the classical thermodynamics by mental experiments is now taken over in the quantum theory by P. Ehrenfest's hypothesis of the adiabatic invariance; and just as the principle introduced by R. Clausius, that any two states of a material system are mutually interconvertible on suitable treatment by reversible processes, formed the basis for the measurement of entropy, just so do the new ideas of Bohr show a way into the midst of the wonderland he has discovered."

"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."

"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."

"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."

"Why is entropy at the beginning of time so low, and the entropy in a black hole so high? ...We ...don't know that the entropy was low ...We don't even know if there was a beginning of time. ...[E]ntropy ...is the physicist's measure of how messy things are, so my room ...tends to get higher and higher entropy, messier and messier. Why... eggs fall on the floor and break, and not... fly up and unbreak? People argued about that for a very long time until the shocking insight... that it was very low 13.4 billion years ago at the time when those... baby pictures of our universe were given off... the cosmic microwave background. ...So somehow, our flow of time towards greater messiness has something to do with our origin of our universe? That... we have learned. ...But now the question of why was that is something where many of my colleagues disagree violently... I have written a paper... which... has very little support... anyway, ...if you take seriously the idea of inflation and also this theory that the does not collapse, according to Hugh Everett, you can do some math and get an explanation... but... it's a wonderful mystery, and I'm open to all ideas... and black holes... is something else we know very little... ultimately where there are great truths yet to be discovered."

"One could... safely declare that 'Physics... can be defined as that subject which treats of the transformation of energy.' The philosophical version of Herakleitos and Empedokles... a continual cycle of changes and exchanges, had... crystallized into a quantitative physical theory. But this... picture... was... incomplete. For... there was a second, equally general and fundamental element in Nature—a directional one. This had first been formulated in the 1820s by the Mozart of modern physics, Sadi Carnot. ...Carnot started with the question: What proportion of the in any system is 'available' as a means of producing ? ...Carnot demonstrated ...a one-hundred-per-cent-efficient engine could exploit only a fraction of the heat supplied to it... A 'super-efficient' machine which could exploit all the heat supplied, would be (as Carnot's mathematics proved) a machine... one could get out of it more energy than was supplied... In an ... physical changes could at most be perfectly reversible; [but] in normal cases they would result in the progressive... 'degradation' of mechanical energy by the production of unavailable heat. To characterize this... Clausius coined the word ... [T]he directional principle of Carnot and Clausias (which gave precise expression to Newton's insight that 'motion is more easily lost than got, and is continually upon the decrease') became the Second Law of Thermodynamics."

"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."

"Entropy continually increases. We can, by isolating parts of the world and postulating rather idealized conditions... arrest the increase, but we cannot turn it into a decrease. ...The law that entropy always increases—the second law of thermodynamics—holds... the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is... found to be against the second law... I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

"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."

"As far as we know, entropy increases throughout the portion of the universe observable from Earth. It does not seem probable to us, but in any case nothing excludes, that beyond the particle horizon which marks the maximum limit of observations there exist regions in which the arrow of time is reversed compared to ours and in which entropy decreases. I dare not think of the theoretical and observational complications that would arise if the matter contained in one of these anomalous regions began to interact with ours."

"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy."

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy."

"Entropy... we shall use this property in a specific and limited manner. ...The following are two implications of this property: 1. If a gas or vapor is compressed or expanded frictionlessly without adding or removing heat during the process, the entropy of the substance remains constant. 2. In the process implied in implication 1, the change in represents the amount of work per unit mass required by the compression or delivered by the expansion. Possibly the greatest possible use we shall have for entropy is to read lines of constant entropy on graphs in computing the work of compression in cycles."

"Entropy is the price of structure."

"I wish I could convey to you the amazing power of this conception of entropy in scientific research. From the property that entropy must always increase, practical methods of measuring it have been found. The chain of deductions from this simple law have been almost illimitable... equally successful in... theoretical physics and the practical tasks of the engineer. ...It is not concerned with the nature of the individual; it is interested in him only as a component of the crowd. ...[T]he method is applicable in fields of research where our ignorance has scarcely begun to lift ..."

"Let's talk some energy transfer principles. ...My Grandpappy always used to say "hot goes to cold." ...Things of a higher energy intensity state tend to equalize with things at a lower intensity energy state. ...Where there's differences, things tend towards equilibrium... You put a ball on top of a hill and you give it a chance to roll down the hill, that's what's going to happen... If you leave a big pile of sand outside long enough, it's going to flatten out. ...You take an ice cube and hold it in your hand ...heat goes out of your hand and melts the ice cube until that water becomes the same temperature as your hand. ...[V]oltage tends toward equilibrium ...If you have this ...high voltage [or current] ...stored in a battery ...[T]ake a wire and hook it from one side to the other ...It's going to equalize ...and the battery's going to be dead ..."