Conservative interacting particles system with anomalous rate of ergodicity

TL;DR

This paper studies a conservative interacting particle system, proving ergodicity and exponential convergence to equilibrium, challenging the common belief that conservative systems only have polynomial convergence rates.

Contribution

It provides a counterexample demonstrating that conservative systems can exhibit exponential convergence, contrary to standard assumptions.

Findings

Proves ergodicity for a specific conservative particle system.

Shows exponential rate of convergence to equilibrium.

Challenges the typical polynomial convergence expectation.

Abstract

We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence.