A generalized integral fluctuation theorem for general jump processes

TL;DR

This paper introduces a generalized integral fluctuation theorem for jump processes using advanced mathematical formulas, unifying existing theorems and providing a new perspective on time-reversal in stochastic systems.

Contribution

It presents a novel GIFT framework for jump processes, connecting it with traditional methods and clarifying the concept of time-reversal in Markovian systems.

Findings

Existing discrete IFTs are special cases of the GIFT.

The approach establishes a natural definition of time-reversal for Markovian systems.

The robust GIFT generally does not imply a detailed fluctuation theorem.

Abstract

Using the Feynman-Kac and Cameron-Martin-Girsanov formulas, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Different from the latter approach that was extensively employed in existing literature, our approach can naturally bring out the definition of a time-reversal of a Markovian stochastic system. Additionally, we find the robust GIFT usually does not result into a detailed fluctuation theorem.