Non-equilibrium fluctuation theorems in the presence of local heating

TL;DR

This paper investigates the validity of non-equilibrium fluctuation theorems, like Crooks' and Jarzynski's, in systems with local heating and explicit heat reservoirs, highlighting conditions for their applicability and effects on convergence.

Contribution

It provides a detailed analysis of the conditions under which fluctuation theorems hold in systems with local heating and explicit reservoirs, extending classical results.

Findings

Fluctuation theorems remain valid despite local heating.

Local heating slows the convergence of exponential work averages.

Conditions for theorem validity are explicitly characterized.

Abstract

We study two non-equilibrium work fluctuation theorems, the Crooks' theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of $<\exp(-\beta W)>$ to its theoretical mean value, where $W$ is the work done on the test system and $\beta$ is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.