Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics

TL;DR

This paper proves a gauge invariance property of the scaled cumulant-generating function in stochastic thermodynamics, enabling more efficient calculations of current statistics in Markovian models.

Contribution

It introduces a gauge invariance proof for asymptotic current statistics, generalizes Schnakenberg's entropy-production decomposition, and provides an efficient computational algorithm.

Findings

Proved gauge invariance of scaled cumulant-generating function.

Developed an efficient algorithm for asymptotic current statistics.

Unified previous theoretical frameworks in stochastic thermodynamics.

Abstract

Stochastic Thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from anti-symmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication.