Stochastic thermodynamics of interacting degrees of freedom: Fluctuation theorems for detached path probabilities

TL;DR

This paper develops a comprehensive framework using detached path probabilities to derive fluctuation theorems for bipartite Markov systems, including special cases like measurement-feedback and hidden Markov models, with applications in model selection.

Contribution

It introduces the concept of detached entropy production for bipartite Markov processes and demonstrates its use in deriving fluctuation theorems and model selection techniques.

Findings

Fluctuation theorems for detached entropy production recover known results in special cases.

The fluctuation relation can be used for model selection in hidden Markov models.

The framework unifies previous approaches using information flow and learning rate.

Abstract

Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a series of special cases including measurement-feedback systems, sensors and hidden Markov models. For these special cases we show that fluctuation theorems involving the detached entropy production recover known results which have been obtained separately before. Additionally, we show that the fluctuation relation for the detached entropy production can be used in model selection for data stemming from a hidden Markov model. We discuss the relation to previous approaches including those which use information flow or learning rate to quantify the influence of one subsystem on the other. In conclusion, we present a complete framework with which to find fluctuation relations for coupled systems.