Fluctuation theorems for harmonic oscillators

TL;DR

This paper experimentally investigates fluctuation theorems in a driven harmonic oscillator, analyzing energy fluctuations during transient and steady states, and derives analytical expressions for the probability distributions of work and heat.

Contribution

It provides the first analytical expression for the probability density function of heat in a harmonic oscillator under non-equilibrium conditions.

Findings

Stationary State Fluctuation Theorem verified for two torque prescriptions.

Transient Fluctuation Theorem holds for work but not for heat with linear forcing.

Excellent agreement between experimental data and theoretical modeling.

Abstract

We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together with non equilibrium steady states. Fluctuations Relations are obtained experimentally for both the work and the heat, for the stationary and transient evolutions. A Stationary State Fluctuation Theorem is verified for the two time prescriptions of the torque. But a Transient Fluctuation Theorem is satisfied for the work given to the system but not for the heat dissipated by the system in the case of linear forcing. Experimental observations on the statistical and dynamical properties of the fluctuation of the angle, we derive analytical expressions for the probability density function of the work and the heat. We obtain for the first time an analytic expression of the probability density function of the heat. Agreement between experiments and our modeling is excellent.