  The work distribution is a fundamental quantity in nonequilibrium
thermodynamics mainly due to its connection with fluctuations theorems. Here we
develop a semiclassical approximation to the work distribution for a quench
process in chaotic systems. The approach is based on the dephasing
representation of the quantum Loschmidt echo and on the quantum ergodic
conjecture, which states that the Wigner function of a typical eigenstate of a
classically chaotic Hamiltonian is equidistributed on the energy shell. We show
that our semiclassical approximation is accurate in describing the quantum
distribution as we increase the temperature. Moreover, we also show that this
semiclassical approximation provides a link between the quantum and classical
work distributions.
