Unifying approach for fluctuation theorems from joint probability distributions

TL;DR

This paper presents a unified framework for deriving fluctuation theorems in Markovian systems based on joint probability distributions, simplifying applications and encompassing various known theorems as special cases.

Contribution

It introduces a generalized approach to fluctuation theorems that does not require dual distributions and applies to a broad class of non-equilibrium steady states.

Findings

Unified fluctuation theorem for joint probability distributions.

Applicable to all times for system and reservoir entropies.

Simplifies derivation of fluctuation theorems without dual distributions.

Abstract

Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time reversal. The expression of the result does not bring into play dual probability distributions, hence easing potential applications. We show that several fluctuation theorems for perturbed non-equilibrium steady states are unified and arise as particular cases of this general result. In particular, we show that the joint probability distribution of the system and reservoir trajectory entropies satisfy a detailed fluctuation theorem valid for all times although each contribution does not do it separately.