Fluctuation Theorem Uncertainty Relation

Yoshihiko Hasegawa and Tan Van Vu
Phys. Rev. Lett. 123, 110602 – Published 12 September 2019
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Abstract

The fluctuation theorem is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations, such as the second law of thermodynamics and the Jarzynski equality. Recently, the thermodynamic uncertainty relation was discovered, which states that the fluctuation of observables is lower bounded by the entropy production. In the present Letter, we derive a thermodynamic uncertainty relation from the fluctuation theorem. We refer to the obtained relation as the fluctuation theorem uncertainty relation, and it is valid for arbitrary dynamics, stochastic as well as deterministic, and for arbitrary antisymmetric observables for which a fluctuation theorem holds. We apply the fluctuation theorem uncertainty relation to an overdamped Langevin dynamics for an antisymmetric observable. We demonstrate that the antisymmetric observable satisfies the fluctuation theorem uncertainty relation but does not satisfy the relation reported for current-type observables in continuous-time Markov chains. Moreover, we show that the fluctuation theorem uncertainty relation can handle systems controlled by time-symmetric external protocols, in which the lower bound is given by the work exerted on the systems.

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  • Received 3 March 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.110602

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Yoshihiko Hasegawa* and Tan Van Vu

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

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

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Issue

Vol. 123, Iss. 11 — 13 September 2019

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