Open Conference Systems, StatPhys 27 Main Conference

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The Stochastic Uncertainty Principle
Jean-Charles Delvenne, Gianmaria Falasco, Massimiliano Esposito

##manager.scheduler.building##: Edificio San Jose
##manager.scheduler.room##: Auditorio 1
Date: 2019-07-11 05:45 PM – 06:00 PM
Last modified: 2019-06-10

Abstract


In a stochastic process satisfying detailed balance, any observable that is anti-symmetric with respect to time reversal, such as total work extracted along the path, has zero mean. Away from equilibrium however, such observables may exhibit a non-zero mean. One way to appreciate the amplitude of this mean is to compare it with the amplitude of the typical fluctuations, in the form of the adimensional square-mean-to-variance ratio.

Barato and Seifert (2015) proposed an upper bound of this ratio over all observables of interests, in terms of the entropy production of the process (defined as the Kullback-Leibler divergence of the process with respect to the time-reversed process). Since then, numerous contributions have proved bounds with various degrees of generality, with diverse arguments from large deviation and information theories mainly.

We introduce a new argument of elementary nature and flexible applicability that allows to formally derive formally the tightest possible bound for a given family of observables of a given stochastic process---which we call the Stochastic Uncertainty Principle.

In particular we recover a result by Proesmans and Van den Broeck (2017) and by Hasegawa and Van Vu (2019). We tighten it to the best bound expressible with entropy alone, and broaden its scope of applicability.

We also consider the case of stationary processes, where we recover some of the known bounds for current-like observables, and propose new bounds for the case of Markov chains.