Fluctuation Theorems for Heat exchanges between passive and active baths

TL;DR

This study uses fluctuation theorems to measure and compare the effective temperature of an active bath in a nonequilibrium setting, revealing differences based on heat definitions and particle jump behavior.

Contribution

It demonstrates that fluctuation theorems can be applied to active baths and shows how different heat definitions affect the inferred temperature in nonequilibrium conditions.

Findings

Fluctuation theorem holds for both equilibrium and active baths.

Effective temperature matches kinetic temperature with one heat definition.

Active bath temperature differs depending on heat measurement approach.

Abstract

In addition to providing general constraints on probability distributions, fluctuation theorems allow to infer essential information on the role played by temperature in heat exchange phenomena. In this numerical study, we measure the temperature of an out of equilibrium active bath using a fluctuation theorem that relates the fluctuations of the heat exchanged between two baths to their temperatures. Our setup consists of a single particle moving between two wells of a quartic potential accommodating two different baths. The heat exchanged between the two baths is monitored according to two definitions: as the kinetic energy carried by the particle whenever it jumps from one well to the other and as the work performed by the particle on one of the two baths when immersed in it. First, we consider two equilibrium baths at two different temperatures and verify that a fluctuation theorem featuring the baths temperatures holds for both heat definitions. Then, we introduce an additional Gaussian coloured noise in one of the baths, so as to make it effectively an active (out-of-equilibrium) bath. We find that a fluctuation theorem is still satisfied with both heat definitions. Interestingly, in this case the temperature obtained through the fluctuation theorem for the active bath corresponds to the kinetic temperature when considering the first heat definition, while it is larger with the second one. We interpret these results by looking at the particle jump phenomenology.