Single active particle in a harmonic potential: non-existence of the Jarzynski relation

TL;DR

This paper demonstrates that the Jarzynski relation does not generally hold for a single active particle in a harmonic potential when using standard stochastic thermodynamics definitions, highlighting fundamental differences from equilibrium thermodynamics.

Contribution

It shows the non-validity of the Jarzynski relation in active matter systems modeled by an active Ornstein-Uhlenbeck particle, revealing limitations of existing thermodynamic relations.

Findings

Jarzynski relation fails for active Ornstein-Uhlenbeck particles.

Standard stochastic thermodynamics definitions of work are insufficient.

Active matter systems require new thermodynamic frameworks.

Abstract

The interest in active matter stimulates the need to generalize thermodynamic description and relations to active matter systems, which are intrinsically out of equilibrium. One important example is the Jarzynski relation, which links the exponential average of work done in an arbitrary process connecting two equilibrium states with the difference of the free energies of these states. Using a simple model system, a single thermal active Ornstein-Uhlenbeck particle in a harmonic potential, we show that if the standard stochastic thermodynamics definition of work is used, the Jarzynski relation is not generally valid for processes between stationary states of active matter systems.