Thermodynamical analysis of a quantum heat engine based on harmonic oscillators

Andrea Insinga, Bjarne Andresen, and Peter Salamon
Phys. Rev. E 94, 012119 – Published 15 July 2016

Abstract

Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

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  • Received 11 April 2016

DOI:https://doi.org/10.1103/PhysRevE.94.012119

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Andrea Insinga* and Bjarne Andresen

  • Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

Peter Salamon

  • Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA

  • *Email addresses: andreainsinga@gmail.com
  • Email addresses: andresen@nbi.ku.dk
  • Email addresses: salamon@math.sdsu.edu

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Issue

Vol. 94, Iss. 1 — July 2016

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