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.

Citation

Marcantoni, S., Pérez-Espigares, C., & Garrahan, J. P. (2020). Symmetry-induced fluctuation relations for dynamical observables irrespective of their behavior under time reversal. Physical Review E, 101(6), Article 062142. https://doi.org/10.1103/physreve.101.062142

• 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