  We have derived several relations, which allow the evaluation of the system
free energy changes in the leading order in $\hbar^{2}$ along classically
generated trajectories. The results are formulated in terms of purely classical
Hamiltonians and trajectories, so that semiclassical partition functions can be
computed, e.g., via classical molecular dynamics simulations. The Hamiltonians,
however, contain additional potential-energy terms, which are proportional to
$\hbar^{2}$ and are temperature-dependent. We discussed the influence of
quantum interference on the nonequilibrium work and problems with unambiguous
definition of the semiclassical work operator.
