Reconsidering the Concept of Equilibrium in Classical Statistical Mechanics

Philosophy of Science 66:S107 - S118 (1999)
In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to account for the non- equilibrium part of the laws of thermodynamics. Rather, we have to weaken the requirement that equilibrium be identified with a stationary probability distribution
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Harvey R. Brown & Jos Uffink (2001). The Origins of Time-Asymmetry in Thermodynamics: The Minus First Law. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):525-538.

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