Fluctuation-response inequality out of equilibrium

Proceedings of the National Academy of Sciences of the United States of America
Andreas Dechant, Shin-ichi Sasa

Abstract

We present an approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that the magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and the unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady-state particle transport, the differential mobility is bounded by the diffusivity. For a "virtual" perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady-state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfi...Continue Reading

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Citations

Sep 18, 2020·Nature Communications·Cheng YangHaibin Wu
Aug 17, 2020·Physical Review. E·Lukas P FischerUdo Seifert
Aug 17, 2020·Physical Review Letters·Yoshihiko Hasegawa
Jul 22, 2020·Physical Review. E·Shun OtsuboTakahiro Sagawa
Nov 27, 2020·Biophysics and Physicobiology·Akihiko Ishijima, Yasushi Okada
Jan 16, 2021·Physical Review Letters·Timur Koyuk, Udo Seifert
Jan 21, 2021·Physical Review. E·Van Tuan VoYoshihiko Hasegawa
Jan 23, 2021·Physical Review Letters·Yoshihiko Hasegawa
Feb 20, 2021·Physical Review. E·Trevor GrandPreDavid T Limmer
Feb 20, 2021·Physical Review. E·Antoine Rignon-BretMark T Mitchison
Apr 10, 2021·The Journal of Chemical Physics·Yonghyun Song, Changbong Hyeon
Jun 11, 2021·Physical Review Letters·Yohei Nakayama, Shoichi Toyabe
Jun 18, 2021·Physical Review. E·Ken Hiura, Shin-Ichi Sasa
Sep 4, 2021·Physical Review Letters·David Hartich, Aljaž Godec

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