Thermalization in open classical systems with finite heat baths

TL;DR

This paper investigates how a harmonic oscillator coupled to a finite heat bath thermalizes, revealing that complete thermalization depends on the oscillator's frequency and mass ratio, with implications for nanomechanical systems.

Contribution

It demonstrates the conditions under which a finite heat bath can fully thermalize a test oscillator, highlighting frequency and mass ratio dependencies.

Findings

Thermalization occurs only within specific frequency ranges.

Complete thermalization depends on the mass ratio.

Implications for nanomechanical resonator behavior.

Abstract

We discuss thermalization of a test particle schematized as a harmonic oscillator and coupled to a Boltzmann heat bath of finite size and with a finite bandwidth for the frequencies of its particles. We find that complete thermalization only occurs when the test particle frequency is within a certain range of the bath particle frequencies, and for a certain range of mass ratios between the test particle and the bath particles. These results have implications for the study of classical and quantum behaviour of high-frequency nanomechanical resonators.