Symmetry-induced fluctuation relations for dynamical observables irrespective of their behavior under time reversal

Marcantoni, Stefano; P�rez-Espigares, Carlos; Garrahan, Juan P.

Abstract

We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behavior under time reversal, for example for time-symmetric observables rather than currents. We further show how to deduce in the long-time limit these FRs from the symmetry properties of the generator of the dynamics. We illustrate our results with four examples that highlight the novel features of our work.

• Journal Article Type: Article
• Acceptance Date: Jun 5, 2020
• Online Publication Date: Jun 26, 2020
• Publication Date: Jun 26, 2020
• Deposit Date: Aug 4, 2020
• Publicly Available Date: Aug 4, 2020
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 101
• Issue: 6
• Article Number: 062142
• DOI: https://doi.org/10.1103/physreve.101.062142
• Public URL: https://nottingham-repository.worktribe.com/output/4810670
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.062142