Fluctuation Relation for Quantum Heat Engines and Refrigerators

Abstract

At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoires of temperatures $T_C\le T_H$ can overperform the ideal Carnot engine: $⟨W⟩/⟨Q_H⟩\le 1-T_C/T_H$. This inequality follows from an exact fluctuation relation involving the nonequilibrium work $W$ and heat exchanged with the hot bath $Q_H$. In a previous work [Sinitsyn N A, J. Phys. A: Math. Theor. {\bf 44} (2011) 405001] this fluctuation relation was obtained under the assumption that the heat engine undergoes a stochastic jump process. Here we provide the general quantum derivation, and also extend it to the case of refrigerators, in which case Carnot's statement reads: $⟨Q_C⟩/|⟨W⟩|\le (T_H/T_C-1{)}^{-1}$.

6 pages, 1 figure. Wrong signs amended in v2

References in corpus (5)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Single ion heat engine with maximum efficiency at maximum power
• Fluctuation theorems in driven open quantum systems
• Fluctuation theorems for continuously monitored quantum fluxes
• Single Particle Stochastic Heat Engine

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