  Usually the calculation of work distributions in an arbitrary nonequilibrium
process in a quantum system, especially in a quantum many-body system is
extremely cumbersome. For all quantum systems described by quadratic
Hamiltonians, we invent a universal method for solving the work distribution of
quantum systems in an arbitrary driving process by utilizing the
group-representation theory. This method enables us to efficiently calculate
work distributions where previous methods fail. In some specific models, such
as the time-dependent harmonic oscillator, the dynamical Casimir effect, and
the transverse XY model, the exact and analytical solutions of work
distributions in an arbitrary nonequilibrium process are obtained. Our work
initiates the study of quantum stochastic thermodynamics based on
group-representation theory.
