Dresden 2017 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 2: Stochastic thermodynamics and information processing

DY 2.2: Vortrag

Montag, 20. März 2017, 10:00–10:15, HÜL 186

Stochastic thermodynamics based on incomplete information: Generalized Jarzynski equality with measurement errors with or without feedback — •Christopher Wächtler, Philipp Strasberg, and Tobias Brandes — Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany

In the derivation of fluctuation relations, and in stochastic thermodynamics in general, it is tacitly assumed that we can measure the system perfectly, i.e., without measurement errors. We here demonstrate for a driven system immersed in a single heat bath, for which the classic Jarzynski equality [1] holds, how to relax this assumption. Based on a general measurement model akin to Bayesian inference we derive a general expression for the fluctuation relation of the measured work and we study the case of an overdamped Brownian particle in particular. We then generalize our results further and incorporate feedback in our description. We argue that, if measurement errors are fully taken into account by the agent who controls and observes the system, the standard Jarzynski-Sagawa-Ueda relation [2] should be formulated differently. We again explicitly demonstrate this for an overdamped Brownian particle where the fluctuation relation of the measured work differs significantly from the efficacy parameter [2]. Instead, the generalized fluctuation relation under feedback control, < e^{−β(W−Δ F)−I}> = 1, holds only for a superobserver having perfect access to both the system and detector degrees of freedom.

[1] C. Jarzynski, PRL 78, 2690 (1997).

[2] T. Sagawa and M. Ueda, PRL 104, 090602 (2010).