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Mind the Gap: Boltzmannian vs Gibbsian EquilibriumThere are two main theoretical frameworks in statistical mechanics, one associated with Boltzmann and the other with Gibbs. Despite their well-known differences, there is the prevailing view that equilibrium values calculated in both frameworks coincide. We show that this is wrong. There are important cases where the Boltzmannian and Gibbsian equilibrium concepts yield different outcomes. Furthermore, the conditions under which equilibria exists are different for Gibbsian and Boltzmannian statistical mechanics. There are, however, special circumstances under which it is true that the equilibrium values coincide. We prove a new theorem offering such circumstances.
University of Salzburg
Philosophy, Logic and Scientific Method