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Quantum Jarzynski equality of measurement-based work extraction

Yohei Morikuni*

Hiroyasu Tajima†

Naomichi Hatano‡

  • Department of Physics, The University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan

  • Department of Physics, The University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan and Center for Emergent Matter Science (CEMS), RIKEN, Wako, Saitama 351-0198, Japan

  • Institute of Industrial Science, The University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan

  • *morikuni@iis.u-tokyo.ac.jp
  • †hiroyasu.tajima@riken.jp
  • ‡hatano@iis.u-tokyo.ac.jp
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Phys. Rev. E 95, 032147 – Published 31 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032147

Abstract

Many studies of quantum-size heat engines assume that the dynamics of an internal system is unitary and that the extracted work is equal to the energy loss of the internal system. Both assumptions, however, should be under scrutiny. In the present paper, we analyze quantum-scale heat engines, employing the measurement-based formulation of the work extraction recently introduced by Hayashi and Tajima [M. Hayashi and H. Tajima, arXiv:1504.06150]. We first demonstrate the inappropriateness of the unitary time evolution of the internal system (namely, the first assumption above) using a simple two-level system; we show that the variance of the energy transferred to an external system diverges when the dynamics of the internal system is approximated to a unitary time evolution. Second, we derive the quantum Jarzynski equality based on the formulation of Hayashi and Tajima as a relation for the work measured by an external macroscopic apparatus. The right-hand side of the equality reduces to unity for “natural” cyclic processes but fluctuates wildly for noncyclic ones, exceeding unity often. This fluctuation should be detectable in experiments and provide evidence for the present formulation.

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Phys. Rev. E 95, 032147– Published 31 March, 2017
  • Received 24 October 2016

©2017 American Physical Society

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