  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 the slabs. This system constitutes a
photonic heat engine that converts radiative heat into work done by the
non-equilibrium lateral Casimir force. Reversely, 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 a photonic heat engine and pump via the fluctuational electrodynamics
formalism. The propulsion force due to the non-reciprocity and the drag force
due to the Doppler effect was revealed as the physical mechanism behind the
heat engine. We also show that in the case of the heat pump, the use of
nonreciprocal materials can help reduce the required velocity. We present an
ideal material dispersion to reach the Carnot efficiency limit. Furthermore, we
derive a relativistic version of the thermodynamic efficiency for our heat
engine and prove that it is bounded by the Carnot efficiency that is
independent of the frame of reference. 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.
