Abstract
We study stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency greater than Carnot’s efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) are illustrated by means 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 implementations with Cooper-pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events.
Highlights
The field of non equilibrium quantum thermodynamics has received a large impulse in the last two decades due to the discovery of a number of exact relations which characterise the response of physical systems, to external perturbations, namely applied mechanical forces or thermodynamic forces. [1, 2]Unlike traditional thermodynamics [3], which focusses on macroscopic quantities, fluctuation relations focus on their microscopic, fluctuating, counterparts
Based on a previous work [42], we have here presented a detailed discussion of fluctuation relations for heat and work in quantum heat engines
We studied its full stochastic energetic exchanges including the statistics of its efficiency
Summary
The field of non equilibrium quantum thermodynamics has received a large impulse in the last two decades due to the discovery of a number of exact relations which characterise the response of physical (possibly small) systems, to external perturbations, namely applied mechanical forces or thermodynamic forces (e.g. temperature gradients, and chemical potential gradients). [1, 2]. We shall remark that in those experiments all quantum coherences are suppressed Another very ingenious method, which is well suited for obtaining the work statistics of a driven system, requires a special coupling of the driven system to an ancilla, e.g. a qubit, and replaces the two energy measurements with state tomography of the qubit at the sole final time [20, 21]. The method is well suited for simultaneously measuring both heat and work in a driven quantum system which stays in contact with one or more baths For this reason it is very promising for the experimental study of the stochastic energy exchange of quantum thermal machines. In the long time limit, steady-state fluctuation relations hold which are independent of the border choice
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