Rethinking Boltzmannian Equilibrium

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Werndl, Charlotte; Frigg, Roman
conference paper description
Boltzmannian statistical mechanics partitions the phase space into macro- regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann's combinatorial argument, the Maxwell-Boltzmann distribution, and maximum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which the system spends most of its time and prove a new theorem establishing that equilibrium thus defined corresponds to the largest macroregion. Our derivation is completely general in that it does not rely on assumptions about the system's dynamics or internal interactions.