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

Garrahan, Juan P. (2017) Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables. Physical Review E, 95 (3). 032134-1-032134/7. ISSN 2470-0053

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Physics and Astronomy
Identification Number: 10.1103/PhysRevE.95.032134
Depositing User: Eprints, Support
Date Deposited: 28 Apr 2017 13:38
Last Modified: 12 Oct 2017 14:51
URI: http://eprints.nottingham.ac.uk/id/eprint/42408

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