On the (Boltzmann) Entropy of Nonequilibrium Systems

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 $\mathcal{H}$-theorem.

31 pages, in Tex, authors' e-mails: [email protected], [email protected]

References in corpus (3)

• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
• Stationary Nonequilibrium States in Boundary Driven Hamiltonian Systems: Shear Flow

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