Energetics of a driven Brownian harmonic oscillator

TL;DR

This paper investigates the energy dynamics of a driven Brownian harmonic oscillator, analyzing energy flow, fluctuation relations, and the effects of damping and inertia in non-equilibrium steady states.

Contribution

It provides a comprehensive analysis of the energetics, fluctuation theorems, and the impact of damping regimes for a driven Brownian oscillator, including new insights into energy flow and fluctuation relations.

Findings

Derived energy balance and flow equations.

Validated Jarzynski fluctuation relation.

Analyzed overdamped and strongly damped regimes.

Abstract

We provide insights into energetics of a Brownian oscillator in contact with a heat bath and driven by an external unbiased time-periodic force that takes the system out of thermodynamic equilibrium. Solving the corresponding Langevin equation, we compute average kinetic and potential energies in the long-time stationary state. We also derive the energy balance equation and study the energy flow in the system. In particular, we identify the energy delivered by the external force, the energy dissipated by a thermal bath and the energy provided by thermal equilibrium fluctuations. Next, we illustrate Jarzynski work-fluctuation relation and consider the stationary state fluctuation theorem for the total work done on the system by the external force. Finally, by determining time scales in the system, we analyze the strong damping regime and discuss the problem of overdamped dynamics when inertial effects can be neglected.