  Using the scaling relation of the ground state quantum fidelity, we propose
the most generic scaling relations of the irreversible work (the residual
energy) of a closed quantum system at absolute zero temperature when one of the
parameters of its Hamiltonian is suddenly changed; we consider two extreme
limits namely, the heat susceptibility limit and the thermodynamic limit. It is
then argued that the irreversible entropy generated for a thermal quench at low
enough temperature when the system is initially in a Gibbs state, is likely to
show a similar scaling behavior. To illustrate this proposition, we consider
zero-temperature and thermal quenches in one and two-dimensional Dirac
Hamiltonians where the exact estimation of the irreversible work and the
irreversible entropy is indeed possible. Exploiting these exact results, we
then establish: (i) the irreversible work at zero temperature indeed shows an
appropriate scaling in the thermodynamic limit; (ii) the scaling of the
irreversible work in the 1D Dirac model at zero-temperature shows logarithmic
corrections to the scaling which is a signature of a marginal situation. (iii)
Furthermore, remarkably the logarithmic corrections do indeed appear in the
scaling of the entropy generated if temperature is low enough while disappears
for high temperatures. For the 2D model, no such logarithmic correction is
found to appear.
