Thermodynamic uncertainty relations constrain non-equilibrium fluctuations

An Author Correction to this article was published on 09 March 2020

This article has been updated


In equilibrium thermodynamics, there exists a well-established connection between dynamical fluctuations of a physical system and the dissipation of its energy into an environment. However, few similarly quantitative tools are available for the description of physical systems out of equilibrium. Here, we offer our perspective on the recent development of a new class of inequalities known as thermodynamic uncertainty relations, which have revealed that dissipation constrains current fluctuations in steady states arbitrarily far from equilibrium. We discuss the stochastic thermodynamic origin of these inequalities, and highlight recent efforts to expand their applicability, which have focused on connections between current fluctuations and the fluctuation theorems.

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Fig. 1: Thermodynamic constraints on fluctuations in particle currents.

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  • 09 March 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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We gratefully acknowledge our collaborators on this work, J. England, N. Perunov, G. M. Rostkoff, K. Proesmans, H. Vroylandt, J. Li, N. Fakhri, R. Marsland III and W. Cui.

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Correspondence to Jordan M. Horowitz or Todd R. Gingrich.

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Peer review information Nature Physics thanks Shin-ichi Sasa and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Horowitz, J.M., Gingrich, T.R. Thermodynamic uncertainty relations constrain non-equilibrium fluctuations. Nat. Phys. 16, 15–20 (2020).

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