Fluctuation-response inequality out of equilibrium

Andreas Dechant, Shin Ichi Sasa

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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 satisfied with equality.

Original languageEnglish
Pages (from-to)6430-6436
Number of pages7
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number12
Publication statusPublished - 2020 Mar 24


  • Entropy
  • Nonequilibrium thermodynamics
  • Response
  • Transport

ASJC Scopus subject areas

  • General

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