99-37 Elliott H. Lieb and Jakob Yngvason
The Mathematics and Physics of the Second Law of Thermodynamics (387K, plain TeX, 93pp. 8eps figures, gzipped tar file) Jan 30, 99
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Abstract. The essential postulates of classical thermodynamics are formu- lated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence, states that given any two states of the same chemical composition at least one is adiabatically accessible from the other) and we show that it can be derived from some assumptions about the pressure and thermal equilibrium. Temperature is derived from entropy, but at the start not even the concept of `hotness' is assumed. Our for- mulation offers a certain clarity and rigor that goes beyond most textbook discussions of the second law.

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