Work extremum principle: Structure and function of quantum heat engines

Abstract

We consider a class of quantum heat engines consisting of two subsystems interacting via a unitary transformation and coupled to two separate baths at different temperatures $T_h>T_c$. The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addition, its efficiency is bounded from below by the Curzon-Ahlborn value $1-\sqrt{T_c/T_h}$ and from above by the Carnot value $1-(T_c/T_h)$. The latter is reached|at finite power|for a macroscopic engine, while the former is achieved in the equilibrium limit $T_h\to T_c$. When the work is maximized at a zero power, even a small (few-level) engine extracts work right at the Carnot efficiency.

16 pages, 5 figures

References in corpus (3)

• Quantum Thermodynamic Cycles and quantum heat engines
• The second law, Maxwell's daemon and work derivable from quantum heat engines
• Small quantum networks operating as quantum thermodynamic machines

Cited by in corpus (6)

• Quantum Thermodynamic Cycles and quantum heat engines
• Quantum Thermodynamic Cycles and Quantum Heat Engines (II)
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• Stochastic pumping of heat: Approaching the Carnot efficiency
• Molecular kinetic analysis of a finite-time Carnot cycle
• Thermodynamics of enhanced heat transfer: a model study