2003/04/30 by Sheldon Goldstein, S. Goldstein, Joel L. Lebowitz · 1 citation
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Phase Equilibria and Thermodynamics #Statistical Mechanics and Entropy #astro-ph #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physd.2004.01.008
published as Physica D193 (2004) 53-66 · 31 pages, in Tex, authors' e-mails: [email protected], [email protected]
arxiv created 2003/06/25 · openalex publication_date 2004/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.