Estimates of the Derivative of the Entropy of Gaussian Thermostats

TL;DR

This paper investigates how the entropy of Gaussian thermostats applied to Anosov geodesic flows varies, establishing that the entropy reaches a local maximum at the geodesic flow.

Contribution

It provides new estimates for the derivative of the entropy map in Gaussian thermostats, showing the geodesic flow as a local maximum of entropy.

Findings

Entropy of geodesic flow is a local maximum.

Derived estimates for the derivative of the entropy map.

Enhanced understanding of thermodynamic properties of Anosov flows.

Abstract

We consider a variation of an Anosov geodesic flow by Gaussian Thermostats and we obtain estimates of the derivative of the entropy map at the geodesic flow. In particular, we prove that the entropy of the geodesic flow is a local maximum for the entropy map.