title: Macrostate equivalence of two general ensembles and specific relative entropies.
abstract: The two criteria of ensemble equivalence, i.e., macrostate equivalence and measure equivalence, are investigated for a general pair of states. Macrostate equivalence implies the two ensembles are indistinguishable by the measurement of macroscopic quantities obeying the large-deviation principle, and measure equivalence means that the specific relative entropy of these two states vanishes in the thermodynamic limit. It is shown that measure equivalence implies a macrostate equivalence for a general pair of states by deriving an inequality connecting the large-deviation rate functions to the specific relative Renyi entropies. The result is applicable to both quantum and classical systems. As applications, a sufficient condition for thermalization, the time scale of quantum dynamics of macrovariables, and the second law with strict irreversibility in a quantum quench are discussed.
authors.affiliation: Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Mori