Abstract
Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics. In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works. In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents and entropy production rate. We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents. We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics. We finally use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier. For the machines considered here, we also perform an optimisation of the system parameters using an algorithm of reinforcement learning.
Highlights
Quantum thermodynamics is the study of out-ofequilibrium thermodynamic phenomena at the quantum scale and has proven an exciting and productive area of research with a large overlap with other areas like quantum information [1,2,3,4,5,6] and stochastic thermodynamics [7,8]
We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents
We use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier
Summary
Quantum thermodynamics is the study of out-ofequilibrium thermodynamic phenomena at the quantum scale and has proven an exciting and productive area of research with a large overlap with other areas like quantum information [1,2,3,4,5,6] and stochastic thermodynamics [7,8]. We show that one can build efficient thermal devices consisting of quantum rotors that interact through a clock model Hamiltonian, as. It has been shown that the chiral version of the clock model in contact with multiple baths at different temperatures, can convert heat currents into rotational motion This conversion is the result of the lack of rotational symmetry in the Hamiltonian and of thermal equilibrium, with the device working as an autonomous thermal motor both in the classical [69,70] and in the quantum regime [71]. In particular we utilize the differential evolution approach [73,74] to find optimum parameter choices Such a scheme, called reinforcement learning, has been used, e.g., to find the optimal network topology in interacting electronic systems working as thermoelectric nanoscale engines [75].
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