Relaxation times for Hamiltonian systems

TL;DR

This paper introduces a new approach to estimating relaxation times in Hamiltonian systems, providing a lower bound and applying it to a model that aligns with observed relaxation times in dilute gases.

Contribution

It offers a novel theoretical framework for relaxation times in Hamiltonian systems and derives a lower bound applicable to interacting gas models.

Findings

Lower bound for relaxation time derived

Application to a concrete gas model

Bound matches observed relaxation times in dilute gases

Abstract

Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition itself of a relaxation time is an open question. We introduce a lower bound for the relaxation time, and give a general theorem for estimating it. Then we give an application to a concrete model of an interacting gas, in which the lower bound turns out to be of the order of magnitude of the relaxation times observed in dilute gases.