Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments

We study stochastic energetic exchanges in quantumheat engines. Due tomicroreversibility, these obey a fluctuation relation, called the heat enginefluctuation relation, which implies the Carnot bound: nomachine can have an efficiency greater thanCarnot’s efficiency. The stochastic thermodynamics of a quantumheat engine (including the joint statistics of heat andwork and the statistics of efficiency) are illustrated bymeans of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits.We discuss possible solid-state implementationswith Cooper-pair boxes andflux qubits, quantumgate operations, and fast calorimetric on-chipmeasurements of single stochastic events.