Quantum to ‘classical’ behaviour in closed-systems thermodynamics: an analysis of the quantum work distribution in driven fermionic chains

The role of many-body interactions in work and entropy production at nanoscales has become a trend topic mainly boosted by increasing interest of probing the laws of thermodynamics for few particle systems. When we turn to the case of strongly correlated systems, one might be interested in probing phase transitions by means of thermodynamical quantities and their statistics, as, for instance, the moments of the so-called quantum work distribution P(W). We propose to examine this question in the context of out-of-equilibrium Hubbard chains by inspecting the extracted work 〈W〉 and the first four central moments 〈W - 〈W〉〉^k , (k=1,2,3,4)$ of P(W). Our analysis inspects the interplay between coupling and dynamical regimes, i.e., we analyse the thermodynamical quantities from non-interacting to the strongly coupled limits when the driving external field is turned on adiabatically or as a sudden quench. Our results indicate a high sensibility of the third momentum (skewness) to the Mott insulator transition and we discuss how it could be used as an order parameter to probe quantum phase transitions in experimental nanoscopic strongly correlated systems.