On applications of Orlicz spaces to statistical physics

Abstract

We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. The pair of Orlicz spaces we explicitly use are, respectively, built on the exponential function (for the description of regular observables) and on an entropic type function (for the corresponding states). They form a dual pair (both for classical and quantum systems). This pair has the advantage of being general enough to encompass regular observables, and specific enough for the latter Orlicz space to select states with a well-defined entropy function. Moreover for small quantum systems, this pair is shown to agree with the classical pairing of bounded linear operators on a Hilbert space, and the trace-class operators.