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The Boltzmann and Gibbs approaches to statistical mechanics have verydifferent definitions of equilibrium and entropy. The problems associated withthis are discussed and it is suggested that they can be resolved, to produce aversion of statistical mechanics incorporating both approaches, by redefiningequilibrium not as a binary property (being/not being in equilibrium) but as acontinuous property (degrees of equilibrium) measured by the Boltzmann entropyand by introducing the idea of thermodynamic-like behaviour for the Boltzmannentropy. The Kac ring model is used as an example to test the proposals.

Boltzmann, Gibbs, and the Concept of Equilibrium