Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound

Naoto Shiraishi and Hiroyasu Tajima
Phys. Rev. E 96, 022138 – Published 16 August 2017

Abstract

A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.

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  • Received 7 January 2017
  • Revised 3 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.022138

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Naoto Shiraishi

  • Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan

Hiroyasu Tajima

  • Center for Emergent Matter Science (CEMS), RIKEN, 2-1 Hirosawa, Wako, 351-0198 Japan

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Issue

Vol. 96, Iss. 2 — August 2017

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