Optimal performance of periodically driven, stochastic heat engines under limited control

Research output: Contribution to journalArticle


  • Michael Bauer
  • Kay Brandner
  • Udo Seifert

Research units

  • University of Stuttgart


We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows us to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.


Original languageEnglish
Article number042112
Pages (from-to)1-14
JournalPhysical Review E
Issue number4
Publication statusPublished - 13 Apr 2016
MoE publication typeA1 Journal article-refereed

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