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Optimal Cycles for Low-Dissipation Heat Engines.

Paolo Abiuso1, Martí Perarnau-Llobet2

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Optimizing finite-time Carnot engines with minimal energy loss reveals a universal optimal operating point. This strategy maximizes power output, which scales with heat capacity for advanced many-body engines.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • Finite-time thermodynamics studies the performance of heat engines operating under realistic time constraints.
  • Carnot engines represent the theoretical upper limit of efficiency for heat engines.
  • Dissipation and finite operating times significantly reduce the performance of real-world engines.

Purpose of the Study:

  • To optimize the performance of a finite-time Carnot engine with small energy losses.
  • To determine the optimal operating strategy and conditions for maximizing engine performance.
  • To investigate the relationship between maximal power output, heat capacity, and engine design.

Main Methods:

  • Derivation of a power bound using a simple inequality.
  • Analysis of optimal cyclic operations around a specific working point.
  • Investigation of dissipative dynamics and their effect on power output.
  • Examination of heat capacity scaling in many-body systems.

Main Results:

  • A simple inequality bounds the power output of the engine.
  • The optimal strategy involves small cycles around an optimally chosen working point.
  • This optimal point is independent of the specific figure of merit (power-efficiency combination) being optimized.
  • Maximal power output is proportional to the heat capacity of the working substance for general dissipative dynamics.
  • Many-body Carnot engines can achieve finite power per constituent at maximum efficiency in the thermodynamic limit.

Conclusions:

  • Optimal operation of finite-time Carnot engines with small dissipations is achievable through small cycles around a universal working point.
  • Maximal power output is directly linked to the working substance's heat capacity, enabling the design of highly efficient many-body engines.
  • This research provides a theoretical framework for designing advanced thermodynamic engines with improved performance characteristics.