 03167 S. Goldstein and Joel L. Lebowitz
 On the (Boltzmann) Entropy of Nonequilibrium Systems
(47K, Tex)
Apr 10, 03

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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 macrovariables, 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 macrovariables
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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