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Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
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Universal Trade-Off Relation between Power and Efficiency for Heat Engines.

Naoto Shiraishi1, Keiji Saito2, Hal Tasaki3

  • 1Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan.

Physical Review Letters
|November 19, 2016
PubMed
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Non-equilibrium thermodynamics shows that any heat current implies energy dissipation. This work proves that heat engines with power output cannot reach Carnot efficiency, establishing a universal trade-off.

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Area of Science:

  • Thermodynamics
  • Non-equilibrium statistical mechanics
  • Physical chemistry

Background:

  • Understanding energy dissipation in thermodynamic systems is crucial.
  • The relationship between efficiency and power in heat engines is a key area of research.
  • Current theories often rely on assumptions of equilibrium or specific symmetries.

Purpose of the Study:

  • To establish a general lower bound for dissipation in thermodynamic systems.
  • To derive a universal trade-off relation between efficiency and power for heat engines.
  • To prove that non-vanishing power in a heat engine precludes Carnot efficiency.

Main Methods:

  • Describing general thermodynamic systems as Markov processes.
  • Developing a theoretical framework for non-equilibrium systems.
  • Proving a lower bound for dissipation based on heat current.

Main Results:

  • A general lower bound for dissipation was proven in terms of the square of the heat current.
  • The existence of a non-vanishing heat current inevitably implies dissipation.
  • A universal trade-off relation between efficiency and power was established.
  • It was rigorously proven that heat engines with non-vanishing power cannot achieve Carnot efficiency.

Conclusions:

  • The findings apply to systems arbitrarily far from equilibrium.
  • The theory does not assume any specific model symmetry.
  • This work provides fundamental insights into the limits of energy conversion in non-equilibrium systems.