A fluctuation theorem for time-series of signal-response models with the backward transfer entropy

TL;DR

This paper establishes a fluctuation theorem linking backward transfer entropy to entropy production in stochastic signal-response models, with applications to linear and nonlinear biological systems, emphasizing the importance of observational time scale.

Contribution

It introduces a new fluctuation theorem connecting backward transfer entropy with entropy production in discretized stochastic models, providing analytical and practical insights.

Findings

Backward transfer entropy bounds conditional entropy production.

Optimal observational time scale is crucial for detecting irreversibility.

Analytical solutions for linear models and applications to receptor-ligand systems.

Abstract

The irreversibility of trajectories in stochastic dynamical systems is linked to the structure of their causal representation in terms of Bayesian networks. We consider stochastic maps resulting from a time discretization with interval \tau of signal-response models, and we find an integral fluctuation theorem that sets the backward transfer entropy as a lower bound to the conditional entropy production. We apply this to a linear signal-response model providing analytical solutions, and to a nonlinear model of receptor-ligand systems. We show that the observational time \tau has to be fine-tuned for an efficient detection of the irreversibility in time-series.