  The thermodynamic behavior of out-of-equilibrium quantum systems in
finite-time dynamics encompasses the description of energy fluctuations, which
dictates a series of system's physical properties. In addition, strong
interactions in many-body systems strikingly affect the energy-fluctuation
statistics along a non-equilibrium dynamics. By driving transient currents to
oppose the precursor to metal-Mott insulator transition in a diversity of
dynamical regimes, we show how increasing correlations dramatically affect the
statistics of energy fluctuations and consequently the quantum work
distribution of finite Hubbard chains. Statistical properties of such
distributions, as its skewness, that changes dramatically across the
transition, can be related to irreversibility and entropy production. Even
close to adiabaticity, the quasi quantum phase transition hinders
equilibration, increasing the process irreversibility, and inducing strong
quantum features in the quantum work distribution. In the Mott-insulating phase
the work fluctuation-dissipation balance gets modified, with the irreversible
entropy production dominating over work fluctuations. The effect of an
interaction-driven quantum-phase-transition on thermodynamics quantities and
irreversibility has to be considered in the design of protocols in small scale
devices for application in quantum technology. Eventually, such many-body
effects can also be employed in work extraction and refrigeration protocols at
quantum scale.
