Abstract
The equilibrium states for an infinite system of classical mechanics may be represented by states over AbelianC* algebras. We consider here continuous and lattice systems and define a mean entropy for their states. The properties of this mean entropy are investigated: linearity, upper semi-continuity, integral representations. In the lattice case, it is found that our mean entropy coincides with theKolmogorov-Sinai invariant of ergodic theory.
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Robinson, D.W., Ruelle, D. Mean entropy of states in classical statistical mechanics. Commun.Math. Phys. 5, 288–300 (1967). https://doi.org/10.1007/BF01646480
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DOI: https://doi.org/10.1007/BF01646480