Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

Garrahan, Juan P.

Abstract

Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.

Citation

Garrahan, J. P. (2017). Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables. Physical Review E, 95(3), Article 032134. https://doi.org/10.1103/physreve.95.032134

• Journal Article Type: Article
• Acceptance Date: Mar 23, 2017
• Online Publication Date: Mar 23, 2017
• Publication Date: Mar 23, 2017
• Deposit Date: Oct 12, 2018
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 3
• Article Number: 032134
• DOI: https://doi.org/10.1103/physreve.95.032134
• Public URL: https://nottingham-repository.worktribe.com/output/1163519
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.032134
• Additional Information: ©2017 American Physical Society. All rights reserved.