Reconsidering the concept of equilibrium in classical statistical mechanics

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In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analog 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 needn't search for alternatives for fine-grained entropy, nor do we have to give up Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, 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.