Dual structure of thermodynamics

Abstract

Based on the properties of exponential distribution families we analyze the Fisher information of the Gibbs canonical ensemble to construct a new state function for simple systems with no mechanical work. Such a function possesses nice symmetry properties with respect to Legendre transform and provides a connection with previous alternative formulations of thermodynamics, most notably the work by Biot, Serrin and Frieden and collaborators. Logical extensions to systems with mechanical work may similarly consider generalized Gibbs ensembles.

Fisher information and Rényi entropies in dynamical systems

“…Even Fisher temperature was defined and Fisher thermodynamics was introduced [2,4,5]. Recently another Fisher thermodynamics has been formulated [6]. It is based on Fisher information with a parameter that is taken the inverse temperature of canonical thermodynamics.…”

“…The layout of this paper is as follows: the following section outlines the alternative formulation of the thermodynamics of Porporato [6]. The Rényi entropies and the spectra of dynamical scaling indices are summarized in Sections III.…”

“…First, the thermodynamic formalism based on Fisher information is summarized [6]. In a canonical ensemble the macrostate of a system is specified by the volume V , the particle number N and the temperature T .…”