Unified approach to classical speed limit and thermodynamic uncertainty relation

Van Tuan Vo, Tan Van Vu, and Yoshihiko Hasegawa
Phys. Rev. E 102, 062132 – Published 15 December 2020

Abstract

The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano-Sasa entropy production. Notably, the obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.

  • Received 1 September 2020
  • Revised 18 November 2020
  • Accepted 19 November 2020

DOI:https://doi.org/10.1103/PhysRevE.102.062132

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Van Tuan Vo*, Tan Van Vu, and Yoshihiko Hasegawa

  • Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan

  • *tuan@biom.t.u-tokyo.ac.jp
  • tan@biom.t.u-tokyo.ac.jp
  • hasegawa@biom.t.u-tokyo.ac.jp

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Issue

Vol. 102, Iss. 6 — December 2020

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