Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time

This work discusses the effects of many-body interactions on the statistics of work in inhomogeneous fermionic chains driven for finite times and across the precursor to the metal-Mott insulator quantum phase transition. For dynamics beyond sudden quenches, a change in sign and a variation in value of the skewness signal the transition, while entropy production dominates work fluctuations even for slow processes, in contrast to the classical work fluctuation dissipation relation.