Thermodynamic phase transitions for Pomeau-Manneville maps

TL;DR

This paper investigates phase transitions in Pomeau-Manneville maps using infinite ergodic theory, providing exact calculations of thermodynamic potentials and linking non-Gaussian fluctuations to algorithmic complexity.

Contribution

It introduces a distributional limit theorem approach to analyze thermodynamic properties and dynamic characteristics of Pomeau-Manneville maps at phase transitions.

Findings

Exact calculations of topological pressure and Renyi entropy.

Connection established between distributional limit theorem and non-Gaussian fluctuations.

Insight into dynamic behavior at instability phases.

Abstract

We study phase transitions in the thermodynamic description of Pomeau-Manneville intermittent maps from the point of view of infinite ergodic theory, which deals with diverging measure dynamical systems. For such systems, we use a distributional limit theorem to provide both a powerful tool for calculating thermodynamic potentials as also an understanding of the dynamic characteristics at each instability phase. In particular, topological pressure and Renyi entropy are calculated exactly for such systems. Finally, we show the connection of the distributional limit theorem with non-Gaussian fluctuations of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad. Sci. USA 85, 4591 (1988)].