Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: An exactly solvable non-dissipative non-ergodic model

TL;DR

This paper presents an exact analytical study of small oscillator systems coupled to finite baths, demonstrating the validity of the Jarzynski equality in non-dissipative, non-ergodic conditions, and introduces a superior analytical method for averaging over initial states.

Contribution

It provides an exact solution for responses of finite bath oscillator systems and shows the Jarzynski equality holds in non-dissipative, non-ergodic regimes, with an improved analytical averaging technique.

Findings

Energy fluctuations are non-dissipative.

Jarzynski equality is valid regardless of force rate.

Analytical method outperforms numerical averaging.

Abstract

Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett (CL) model in which a harmonic oscillator (system) is coupled to finite $N$-body oscillators (bath) with an identical frequency ($\omega_n=\omega_o$ for $n=1$ to $N$). We have derived exact expressions for positions, momenta and energy of the system in nonequilibrium states and for work performed by applied forces. Detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior than numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to finite bath is fluctuating but non-dissipative. It has been shown that the Jarzynski equality (JE) is valid in non-dissipative, non-ergodic open oscillator systems regardless of the rate of applied ramp force.