Relaxation in finite and isolated classical systems: an extension of Onsager's regression hypothesis

TL;DR

This paper extends Onsager's regression hypothesis to finite, isolated classical systems using the microcanonical fluctuation-dissipation theorem, with potential applications in finite-system dynamics and statistical mechanics.

Contribution

It introduces a novel extension of Onsager's relation to finite, isolated systems based on microcanonical fluctuation-dissipation principles.

Findings

Extension derived from microcanonical fluctuation-dissipation theorem

Application demonstrated on a nonintegrable system

Potential relevance to finite system dynamics

Abstract

In order to derive the reciprocity relations, Onsager formulated a relation between thermal equilibrium fluctuations and relaxation widely known as regression hypothesis. It is shown in the present work how such relation can be extended to finite and isolated classical systems. This extension is derived from the fluctuation-dissipation theorem for the microcanonical ensemble. The results are exemplified with a nonintegrable system in order to motivate possible applications to dynamical systems and statistical mechanics of finite systems.