On metastability in nearly-elastic systems

TL;DR

This paper analyzes a nearly-elastic stochastic system with one degree of freedom, deriving its weak limit, large deviation asymptotics, and metastability properties, revealing complex long-term behavior due to small energy exchanges.

Contribution

It introduces a stochastic model for nearly-elastic systems and computes the weak limit and metastability characteristics, advancing understanding of their long-term dynamics.

Findings

Weak limit of the slow motion process on a graph

Large deviation asymptotics for energy fluctuations

Metastability behavior in nearly-elastic systems

Abstract

We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow motion, which is a stochastic process on a graph, is calculated. A large deviation type asymptotics and the metastability of the system are also considered.