Thermodynamic Formalism Out of Equilibrium, and Gibbs Processes

TL;DR

This paper extends thermodynamic formalism to systems with random potentials, defining pressure out of equilibrium and establishing a variational principle, with applications to random dynamical systems driven by Gibbs processes.

Contribution

It introduces the concept of pressure out of equilibrium for random potentials and proves a variational principle, advancing the understanding of non-i.i.d. random dynamical systems.

Findings

Defined pressure out of equilibrium for random potentials

Proved a variational principle for these systems

Established hyperbolicity estimates for Gibbs-driven randomness

Abstract

We study the thermodynamic formalism of systems where the potential depends randomly on an exterior system. We define the {\em pressure out of equilibrium} for such a family of potentials, and prove a corresponding variational principle. We present an application to random dynamical systems. In particular, we study an open condition for random dynamical systems where the randomness is driven by a Gibbs process, and prove hyperbolicity estimates that were previously only known in the i.i.d setting.