Quantum thermodynamics of moving systems

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Παπαδάτος, Νικόλαος
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Abstract
We analyse the thermodynamics of a quantum system in a trajectory of constant velocity that interacts with a static thermal bath. The latter is modeled by a massless scalar field in a thermal state. We consider two different couplings of the moving system to the heat bath, a coupling of the Unruh-DeWitt type and a coupling that involves the time derivative of the field. We derive the master equation for the reduced dynamics of the moving quantum system. It has the same form with the quantum optical master equation, but with different coefficients that depend on velocity. This master equation has a unique asymptotic state for each type of coupling, and it is characterized by a well-defined notion of heat-flow. Our analysis of the second law of thermodynamics leads to a surprising equivalence: a moving heat bath is physically equivalent to a mixture of heat baths at rest, each with a different temperature. There is no unique rule for the Lorentz transformation of temperature. We propose that Lorentz transformations of thermodynamic states are well defined in an extended thermodynamic space that is obtained as a convex hull of the standard thermodynamic space.\\ Additionally, we investigate the quantum thermodynamic cycle of a quantum heat engine carrying out an Otto thermodynamic cycle. We use the thermal properties of a moving heat bath with relativistic velocity with respect to the cold bath. As a working medium, we use a two-level system and a harmonic oscillator that interact with a hot and cold bath respectively. In the current work, the quantum heat engine is studied in the high and low temperatures regime. Using quantum thermodynamics and the theory of open quantum systems we obtain the total produced work, the efficiency and the efficiency at maximum power. The maximum efficiency of the Otto quantum heat engine depends only on the ratio of the minimum and maximum energy gaps. On the contrary, the efficiency at maximum power and the extracted work decreases with the velocity since the motion of the heat bath has an energy cost for the quantum heat engine. Finally, the efficiency at maximum power depends on the nature of the working medium.
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Open quantum systems, Quantum thermodynamics
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