Thermalization of rate-independent processes by entropic regularization

TL;DR

This paper investigates how coupling rate-independent processes with a heat bath through entropic regularization affects their dynamics, transforming them into a non-linear gradient descent with a new dissipation potential.

Contribution

It introduces an entropic regularization approach to thermalize rate-independent processes, revealing how heat baths alter their effective behavior in a controlled manner.

Findings

Heat bath destroys rate independence in a deterministic way

Effective dynamics become a non-linear gradient descent

New dissipation potential characterizes the thermalized process

Abstract

We consider the effective behaviour of a rate-independent process when it is placed in contact with a heat bath. The method used to "thermalize" the process is an interior-point entropic regularization of the Moreau--Yosida incremental formulation of the unperturbed process. It is shown that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are those of a non-linear gradient descent in the original energetic potential with respect to a different and non-trivial effective dissipation potential.