  We develop a general approach for calculating the characteristic function of
the work distribution of quantum many-body systems in a time-varying potential,
whose many-body wave function can be cast in the Slater determinant form. Our
results are applicable to a wide range of systems including an ideal gas of
spinless fermions in one dimension (1D), the Tonks-Girardeau (TG) gas of
hard-core bosons, as well as a 1D gas of hard-core anyons. In order to
illustrate the utility of our approach, we focus on the TG gas confined to an
arbitrary time-dependent trapping potential. In particular, we use the
determinant representation of the many-body wave function to characterize the
nonequilibrium thermodynamics of the TG gas and obtain exact and
computationally tractable expressions---in terms of Fredholm determinants---for
the mean work, the work probability distribution function, the nonadiabaticity
parameter, and the Loschmidt amplitude. When applied to a harmonically trapped
TG gas, our results for the mean work and the nonadiabaticity parameter reduce
to those derived previously using an alternative approach. We next propose to
use periodic modulation of the trap frequency in order to drive the system to
highly non-equilibrium states by taking advantage of the phenomenon of
parametric resonance. Under such driving protocol, the nonadiabaticity
parameter may reach large values, which indicates a large amount of
irreversible work being done on the system as compared to sudden quench
protocols considered previously. This scenario is realizable in ultracold atom
experiments, aiding fundamental understanding of all thermodynamic properties
of the system.
