A system consisting of two slabs with different temperatures can exhibit a non-equilibrium lateral Casimir force on either one of the slabs, when Lorentz reciprocity is broken in at least one of them. This system constitutes a photonic heat engine that converts radiative heat energy into work done by the non-equilibrium Casimir force. Inversely, by sliding two slabs at a sufficiently high relative velocity, heat is pumped from the slab at a lower temperature to the other one at a higher temperature. Hence the system operates as a photonic heat pump. In this work, we study the thermodynamic performance of such photonic heat engine and pump via the exact fluctuational electrodynamics formalism. The propulsion force due to the non-reciprocity and the drag force due to the Doppler effect were revealed as the physical mechanism behind the heat engine. We also show that the heat pump can be achieved only by the Doppler effect and non-reciprocal materials can help further reduce the required velocity to achieve heat pumping. Furthermore, we derive a relativistic version of the thermodynamic efficiency for our heat engine and show that the Carnot limit is independent of the frame of reference. We explore an ideal material dispersion to reach that efficiency. Our work serves as a conceptual guide for the realization of photonic heat engines based on fluctuating electromagnetic fields and relativistic thermodynamics and shows the important role of electromagnetic non-reciprocity in operating them.
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