Effective statistical physics of Anosov systems

TL;DR

This paper proposes a framework to assign a unique effective temperature to Anosov systems, extending thermodynamical formalism to nonequilibrium steady states under the chaotic hypothesis, supported by analyses of the cat map and geodesic flow.

Contribution

It introduces a novel approach to define an effective temperature for Anosov systems, broadening Ruelle's thermodynamical formalism for nonequilibrium states.

Findings

Anosov systems can have a well-defined effective temperature.

The formalism is validated on the cat map and geodesic flow.

Extension of thermodynamical formalism to nonequilibrium states.

Abstract

We present evidence indicating that Anosov systems can be endowed with a unique physically reasonable effective temperature. Results for the two paradigmatic Anosov systems (i.e., the cat map and the geodesic flow on a surface of constant negative curvature) are used to justify a proposal for extending Ruelle's thermodynamical formalism into a comprehensive theory of statistical physics for nonequilibrium steady states satisfying the Gallavotti-Cohen chaotic hypothesis.