Non-equilibrium work fluctuations for oscillators in non-Markovian baths

TL;DR

This paper investigates work fluctuation theorems for oscillators in non-Markovian baths, demonstrating their exact validity for harmonic oscillators and exploring their robustness in anharmonic cases through simulations.

Contribution

It derives the exact validity of fluctuation theorems for non-Markovian oscillators and examines their applicability to anharmonic systems via numerical simulations.

Findings

Jarzynski equality and Crooks' theorem are exact for harmonic oscillators.

Fluctuation theorems remain valid in anharmonic oscillators regardless of bath memory.

Transient fluctuation theorem can fail with asymmetric driving forces and potentials.

Abstract

We study work fluctuation theorems for oscillators in non-Markovian heat baths. By calculating the work distribution function for a harmonic oscillator with motion described by the generalized Langevin equation, the Jarzynski equality (JE), transient fluctuation theorem (TFT), and Crooks' theorem (CT) are shown to be exact. In addition to this derivation, numerical simulations of anharmonic oscillators indicate that the validity of these nonequilibrium theorems do not depend on the memory of the bath. We find that the JE and the CT are valid under many oscillator potentials and driving forces whereas the TFT fails when the driving force is asymmetric in time and the potential is asymmetric in position.