Skip to main content

Research Repository

Advanced Search

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

Garrahan, Juan P.

Authors



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.

Journal Article Type Article
Publication Date Mar 23, 2017
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
APA6 Citation Garrahan, J. P. (2017). Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables. Physical Review E, 95(3), doi:10.1103/physreve.95.032134. ISSN 2470-0045
DOI https://doi.org/10.1103/physreve.95.032134
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.032134
Additional Information ©2017 American Physical Society. All rights reserved.
;