On the (Boltzmann) Entropy of Nonequilibrium Systems

S. Goldstein; Joel L. Lebowitz

doi:10.1016/j.physd.2004.01.008

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arXiv · cond-mat/0304251

On the (Boltzmann) Entropy of Nonequilibrium Systems

S. Goldstein·Joel L. Lebowitz

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Abstract

Boltzmann defined the entropy of a macroscopic system in a macrostate $M$ as the $\log$ of the volume of phase space (number of microstates) corresponding to $M$. This agrees with the thermodynamic entropy of Clausius when $M$ specifies the locally conserved quantities of a system in local thermal equilibrium (LTE). Here we discuss Boltzmann's entropy, involving an appropriate choice of macro-variables, for systems not in LTE. We generalize the formulas of Boltzmann for dilute gases and of Resibois for hard sphere fluids and show that for macro-variables satisfying any deterministic autonomous evolution equation arising from the microscopic dynamics the corresponding Boltzmann entropy must satisfy an ${\cal H}$-theorem.

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BibTeX RIS

S. Goldstein, Joel L. Lebowitz. 2003-06-25. On the (Boltzmann) Entropy of Nonequilibrium Systems. https://doi.org/10.1016/j.physd.2004.01.008

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