Fluctuation theorem for entropy production of a partial system in the weak coupling limit

TL;DR

This paper introduces a new fluctuation theorem for the entropy production of a partial system weakly coupled to another, showing how violations of the steady state fluctuation theorem can reveal such couplings.

Contribution

It presents a novel fluctuation theorem applicable to partial systems under weak coupling, with an analytical demonstration using a realistic model and external random forces.

Findings

Violation of the fluctuation theorem indicates weak coupling presence.

External random forces can induce significant fluctuation theorem violations.

The new theorem applies in the weak coupling limit for small stochastic systems.

Abstract

Small systems in contact with a heat bath evolve by stochastic dynamics. Here we show that, when one such small system is weakly coupled to another one, it is possible to infer the presence of such weak coupling by observing the violation of the steady state fluctuation theorem for the partial entropy production of the observed system. We give a general mechanism due to which the violation of the fluctuation theorem can be significant, even for weak coupling. We analytically demonstrate on a realistic model system that this mechanism can be realized by applying an external random force to the system. In other words, we find a new fluctuation theorem for the entropy production of a partial system, in the limit of weak coupling.