Abstract
For systems of particles in classical phase space with standard Hamiltonian, we consider (spatially averaged) microcanonical Gibbs distributions in finite boxes. We show that infinite-volume limits along suitable subsequences exist and are grand canonical Gibbs measures. On the way, we establish a variational formula for the thermodynamic entropy density, as well as a variational characterization of grand canonical Gibbs measures.
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Georgii, HO. The equivalence of ensembles for classical systems of particles. J Stat Phys 80, 1341–1378 (1995). https://doi.org/10.1007/BF02179874
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DOI: https://doi.org/10.1007/BF02179874