Noncyclic geometric phase in counting statistics and its role as an excess contribution

TL;DR

This paper introduces a fiber bundle framework to analyze counting statistics in stochastic processes, revealing a noncyclic geometric phase linked to excess contributions in nonequilibrium physics, with implications for entropy production.

Contribution

It presents a novel application of fiber bundles to decompose cumulant generating functions into dynamical and geometric phases, highlighting the role of noncyclic geometric phases as excess contributions.

Findings

Noncyclic geometric phase relates to excess entropy production.

Differences identified between geometric contribution and excess entropy production.

Framework applied to a nonequilibrium model to illustrate concepts.

Abstract

We propose an application of fiber bundles to counting statistics. The framework of the fiber bundles gives a splitting of a cumulant generating function for current in a stochastic process, i.e., contributions from the dynamical phase and the geometric phase. We will show that the introduced noncyclic geometric phase is related to a kind of excess contributions, which have been investigated a lot in nonequilibrium physics. Using a specific nonequilibrium model, the characteristics of the noncyclic geometric phase are discussed; especially, we reveal differences between a geometric contribution for the entropy production and the `excess entropy production' which has been used to discuss the second law of steady state thermodynamics.