Entropy (thermodynamics)

"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."

"[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."

"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."

"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."

"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 ..."

"Thermodynamical Equilibrium. Progress of time introduces more of the random element into the constitution of the world. ...[T]he world contains both chance and design, or... antithesis of chance. ...[O]ur method of measurement of entropy: we assign to the organization or non-chance element a measure... proportional to the strength of our disbelief in a chance origin of it. ...The scientific name for a fortuitous concourse of atoms is "thermodynamic equilibrium". ...Thermodynamic equilibrium is the... case... in which no increase in the random element can occur... [i.e.] shuffling is... as thorough as possible. ...In such a region we lose time's arrow. ...[T]he arrow points in the direction of increase of the random element. ...The arrow does not know which direction to point."

"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..."

"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)."

"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."

"[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."

"[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."

"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)."

"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."

"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."

"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."

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

"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."

"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."

"I was interested in the concept introduced by Clausius, entropy.., (in addition to energy,) one of the most important variables of nature."

"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."

"When occurs, entropy has reached... maximum. If entropy can no longer grow.., no change can occur. This... I applied to physical-chemical and to radiation equilibria."

"I did not find the entropy of heat radiation... purely theoretically in the beginning. I only found it by reference to experimental measurements... To interpret these laws... found experimentally.., I was guided by the thoughts of Ludwig Boltzmann.., who was able to interpret the entropy of a from... atomic theory, as the logarithm of the probability of the state of the gas."

"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'."

"What is entropy? ...a measurable physical quantity just like the length ...temperature ...the heat of fusion ...or the specific heat of any given substance. At ... ...the entropy of any substance is zero. When you bring the substance into any other state by slow, reversible little steps ...the entropy increases by an amount computed by dividing every little portion of heat you had to supply ...by the absolute temperature at which it was supplied ...and by summing up all these small contributions."

"[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"

"[T]he device by which an organism maintains itself stationary at a fairly high level of orderliness (...low level of entropy) ...consists in continually sucking orderliness from its environment."

"[H]igher animals... feed upon... the extremely well-ordered state of... foodstuffs. After utilizing it they return it in a... degraded form—not entirely degraded... for plants can... use... it. (...[Plants] have their most powerful supply of 'negative entropy' in the sunlight)."

"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."

"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."

"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."

"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 ..."

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

"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..."

"[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."

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

"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..."

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

"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."

"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'..."

"Suppose we claim... heat flowing in the wrong direction, such as... ice forming in a glass of water... in an oven. ...Energy left the cool... water as heat, so the entropy went down. Because the temperature is low... in the denominator... that decrease in entropy is large. The same energy enters the hot region (...oven), so the entropy of that region increases. However... its temperature is high, [so] that increase in entropy is small. The net effect... a net decrease overall. ...[But] entropy never decreases, so heat cannot flow spontaneously... hot to cold..."

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

"There was considerable opposition... the Second Law... offended the sensibilities of the age... [H]ow can something increase in abundance? ...Who or what is pouring entropy into the universe..?"

"The [Second] law is... used to predict whether a chemical reaction will run in one direction or another..."