On the paradoxical behavior of a cyclic device working with a non-Boltzmannian fluid

According to standard thermodynamics, the efficiency of a cyclic machine is strictly lower than one. Such a result is a straightforward consequence of the second principle of thermodynamics. Recent advances in the study of the thermodynamics of long-range interacting system report however on a rather intricate zoology of peculiar behaviors, which are occasionally in contrast with customarily accepted scenarios, dueling with intuition and common sense. In this paper, a thermodynamical cycle is assembled for an ideal device working with non-Boltzmanian long-range fluid and operating in contact with two thermal reservoirs. Assuming the microcanonical or canonical temperature to be the correct thermodynamic temperature, we obtain a paradoxical conclusion: the system is in fact analytically shown to violate the second principle of thermodynamics. This phenomenon ultimately relates to the existence of regions in the canonical ensemble where the energy decreases with the average kinetic temperature. We argue that the validity of the second principle of thermodynamics can be possibly regained, by revisiting the definition of canonical ensemble, as well as the Fourier law of heat transport, and consequently relaxing the constraint on the maximal efficiency as imposed by the Carnot theorem.