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Nonequilibrium thermodynamics of feedback control

Takahiro Sagawa1,2 and Masahito Ueda3,4

  • 1Hakubi Center, Kyoto University, Yoshida-ushinomiya cho, Sakyo-ku, Kyoto 606-8302, Japan
  • 2Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
  • 3Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 4ERATO Macroscopic Quantum Control Project, JST, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

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Phys. Rev. E 85, 021104 – Published 3 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.021104

Abstract

We establish a general theory of feedback control on classical stochastic thermodynamic systems and generalize nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality in the presence of feedback control with multiple measurements. Our results are generalizations of the previous relevant works to the situations with general measurements and multiple heat baths. The obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control. A generalized Szilard engine and a feedback-controlled ratchet are shown to satisfy the derived equalities.

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Phys. Rev. E 85, 021104– Published 3 February, 2012
  • Received 16 May 2011

©2012 American Physical Society

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