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arXiv · 1701.00539

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

Juan P. Garrahan
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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 non-decreasing 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.

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Juan P. Garrahan. 2017-01-02. Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables. https://doi.org/10.1103/physreve.95.032134

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