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  • Open Access

General Upper Bounds on Fluctuations of Trajectory Observables

George Bakewell-Smith1, Federico Girotti1,2,3, Mădălin Guţă1,2, and Juan P. Garrahan4,2

  • 1School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 2Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 3Department of Mathematics, Polytechnic University of Milan, Milan, Piazza Leonardo da Vinci 32, 20133, Italy
  • 4School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom

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Phys. Rev. Lett. 131, 197101 – Published 8 November, 2023

DOI: https://doi.org/10.1103/PhysRevLett.131.197101

Abstract

Thermodynamic uncertainty relations (TURs) are general lower bounds on the size of fluctuations of dynamical observables. They have important consequences, one being that the precision of estimation of a current is limited by the amount of entropy production. Here, we prove the existence of general upper bounds on the size of fluctuations of any linear combination of fluxes (including all time-integrated currents or dynamical activities) for continuous-time Markov chains. We obtain these general relations by means of concentration bound techniques. These “inverse TURs” are valid for all times and not only in the long time limit. We illustrate our analytical results with a simple model, and discuss wider implications of these new relations.

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Phys. Rev. Lett. 131, 197101– Published 8 November, 2023
  • Received 20 December 2022
  • Accepted 21 September 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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