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Time–information uncertainty relations in thermodynamics

Nature Physics volume 16, pages 1211–1215 (2020)Cite this article

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Abstract

Physical systems powering motion and creating structure in a fixed amount of time dissipate energy and produce entropy. Whether living, synthetic or engineered, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit—a time–information uncertainty relation—imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its s.d. From this general bound, we establish a family of speed limits for heat, dissipated/chemical work and entropy depending on the experimental constraints on the system and its environment. In all of these inequalities, the timescale of transient dynamical fluctuations is universally bounded by the Fisher information. Moreover, they all have a mathematical form that mirrors the Mandelstam–Tamm version of the time–energy uncertainty relation in quantum mechanics. These bounds on the speed of arbitrary observables apply to transient systems away from thermodynamic equilibrium, independent of the physical constraints on the stochastic dynamics or their function.

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Fig. 1: Speed limit from the statistical distinguishability of thermodynamic observables.
Fig. 2: Illustration of time–information uncertainty relation and speed limit for a model of driven assembly of monomeric units.

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Data availability

The data sets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

Code availability

The codes generated and used during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

We acknowledge support from the National Science Foundation under grant no. 1856250 and the US Army Research Laboratory and the US Army Research Office under grant no. W911NF-14-1-0359. This work is further supported by the John Templeton Foundation, UMass Boston project no. P20150000029279, DoE grant no. DE-SC0019515, AFOSR MURI project ‘Scalable Certification of Quantum Computing Devices and Networks’, DoE ASCR Quantum Testbed Pathfinder programme (award no. DE-SC0019040), DoE BES QIS programme (award no. DE-SC0019449), DoE ASCR FAR-QC (award no. DE-SC0020312), NSF PFCQC programme, AFOSR, ARO MURI, ARL CDQI, and NSF PFC at JQI.

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Authors and Affiliations

  1. Department of Chemistry, University of Massachusetts Boston, Boston, MA, USA

    Schuyler B. Nicholson & Jason R. Green

  2. Center for Quantum and Nonequilibrium Systems, University of Massachusetts Boston, Boston, MA, USA

    Schuyler B. Nicholson & Jason R. Green

  3. Department of Physics, University of Massachusetts Boston, Boston, MA, USA

    Luis Pedro García-Pintos, Adolfo del Campo & Jason R. Green

  4. Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST/University of Maryland, College Park, MD, USA

    Luis Pedro García-Pintos

  5. Donostia International Physics Center, San Sebastián, Spain

    Adolfo del Campo

  6. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    Adolfo del Campo

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  1. Schuyler B. Nicholson
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  3. Adolfo del Campo
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S.B.N., L.P.G.P., A.dC. and J.R.G. contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript.

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Correspondence to Jason R. Green.

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Supplementary Figs. 1–4, results and discussion.

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Nicholson, S.B., García-Pintos, L.P., del Campo, A. et al. Time–information uncertainty relations in thermodynamics. Nat. Phys. 16, 1211–1215 (2020). https://doi.org/10.1038/s41567-020-0981-y

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