  We investigate the particle-number dependence of some features of the
out-of-equilibrium dynamics of d-dimensional Fermi gases in the dilute regime.
We consider protocols entailing the variation of the external potential which
confines the particles within a limited spatial region, in particular sudden
changes of the trap size. In order to characterize the dynamic behavior of the
Fermi gas, we consider various global quantities such as the ground-state
fidelity for different trap sizes, the quantum work statistics associated with
the protocol considered, and the Loschmidt echo measuring the overlap of the
out-of-equilibrium quantum states with the initial ground state. Their
asymptotic particle-number dependences show power laws for noninteracting Fermi
gases. We also discuss the effects of short-ranged interactions to the power
laws of the average work and its square fluctuations, within the Hubbard model
and its continuum limit, arguing that they do not generally change the
particle-number power laws of the free Fermi gases, in any spatial dimensions.
