I will investigate unexplored and general features of quantum thermodynamics and applications to quantum thermal machines with systems in the deep quantum regime. Specifically, I will consider thermodynamics processes for the grandcanonical ensemble of gases with Bose-Einstein condensates (BEC), both standard and low dimensional, and of exactly solvable interacting models. These systems have not been considered in the framework of quantum thermodynamics. Furthermore, the grandcanonical ensemble is the statistical ensemble that best captures genuinely quantum effects induced by indistinguishability, like BEC phases. I will therefore investigate thermodinamic processes and cycles, including new genuine quantum cycles, aiming at a deep analysis of ideal reversible cycles, which capture fundamental and dominant effects, and of their discrepancies with respect to real machines, e.g. modelled by endoreversible cycles. I will study both ideal and endoreversible cycles. The latters consist of irreversible heat exchanges modelled by phenomenological entropy production laws. This study will identify thermal processes more efficient when implemented with quantum gases. Specific techniques that I will use are finite size scaling for BEC phases and transitions, perturbative (virial and cluster) expansions for weak interactions, exact solutions of mean-field and weakly interacting Bose gases, local density approximation for unitary Fermi gases, phenomenological entropy production laws and quantum dissipative dynamics to model irreversibility of endoreversible cycles. This general and theoretical research project finds applications in several physical systems, ranging from quantum gases realised with current technology laboratories to novel applications of quantum thermodynamics, like black holes or neutron stars, and of thermo field theory, like dark matter, supersymmetry, and neutrino mixing.

Ugo Marzolino – INFN TRIESTE