Thermodynamics IV

"It is impossible by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. [Footnote: ] If this axiom be denied for all temperatures, it would have to be admitted that a self-acting machine might be set to work and produce mechanical effect by cooling the sea or earth, with no limit but the total loss of heat from the earth and sea, or in reality, from the whole material world." (William Thomson, "On the Dynamical Theory of Heat with Numerical Results Deduced from Mr Joule's Equivalent of a Thermal Unit and M. Regnault's Observations on Steam", Transactions of the Royal Society of Edinburgh, 1851)

"Though the ultimate state of the universe may be its vital and psychical extinction, there is nothing in physics to interfere with the hypothesis that the penultimate state might be the millennium - in other words a state in which a minimum of difference of energy - level might have its exchanges so skillfully canalises that a maximum of happy and virtuous consciousness would be the only result." (William James, [Letter to Henry Adams] 1910)" (William James, [Letter to Henry Adams] 1910)

"Organic evolution has its physical analogue in the universal law that the world tends, in all its parts and particles, to pass from certain less probable to certain more probable configurations or states. This is the second law of thermodynamics." (D'Arcy Wentworth Thompson, "On Growth and Form", 1917)

"In classical physics, most of the fundamental laws of nature were concerned either with the stability of certain configurations of bodies, e.g. the solar system, or else with the conservation of certain properties of matter, e.g. mass, energy, angular momentum or spin. The outstanding exception was the famous Second Law of Thermodynamics, discovered by Clausius in 1850. This law, as usually stated, refers to an abstract concept called entropy, which for any enclosed or thermally isolated system tends to increase continually with lapse of time. In practice, the most familiar example of this law occurs when two bodies are in contact: in general, heat tends to flow from the hotter body to the cooler. Thus, while the First Law of Thermodynamics, viz. the conservation of energy, is concerned only with time as mere duration, the Second Law involves the idea of trend." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

"The second law of thermodynamics provides a more modem (and a more discouraging) example of the maximum principle: the entropy (disorder) of the universe tends toward a maximum." (James R Newman, "The World of Mathematics" Vol. II, 1956)

"[...] thermodynamics knows of no such notion as the 'entropy of a physical system'. Thermodynamics does have the concept of the entropy of a thermodynamic system; but a given physical system corresponds to many different thermodynamic systems." (Edwin T Jaynes, "Gibbs vs Boltzmann Entropies", 1964)

"'You cannot base a general mathematical theory on imprecisely defined concepts. You can make some progress that way; but sooner or later the theory is bound to dissolve in ambiguities which prevent you from extending it further.' Failure to recognize this fact has another unfortunate consequence which is, in a practical sense, even more disastrous: 'Unless the conceptual problems of a field have been clearly resolved, you cannot say which mathematical problems are the relevant ones worth working on; and your efforts are more than likely to be wasted.'" (Edwin T Jaynes, "Foundations of Probability Theory and Statistical Mechanics", 1967)

"There is no end to this search for the ultimate ‘true’ entropy until we have reached the point where we control the location of each atom independently. But just at that point the notion of entropy collapses, and we are no longer talking thermodynamics." (Edwin T Jaynes, "Papers on Probability, Statistics, and Statistical Physics", 1983)

"No one has yet succeeded in deriving the second law from any other law of nature. It stands on its own feet. It is the only law in our everyday world that gives a direction to time, which tells us that the universe is moving toward equilibrium and which gives us a criteria for that state, namely, the point of maximum entropy, of maximum probability. The second law involves no new forces. On the contrary, it says nothing about forces whatsoever." (Brian L Silver, "The Ascent of Science", 1998)