  We construct a novel class of exact solutions to the Boltzmann equation, in
both its classical and quantum formulation, for arbitrary collision laws. When
the system is subjected to a specific external forcing, the precise form of
which is worked out, non equilibrium damping-less solutions are admissible.
They do not contradict the $H$-theorem, but are constructed from its
requirements. Interestingly, these solutions hold for time-dependent
confinement. We exploit them, in a reverse-engineering perspective, to work out
a protocol that shortcuts any adiabatic transformation between two equilibrium
states in an arbitrarily short time-span, for an interacting system. Particle
simulations of the direct Monte Carlo type fully corroborate the analytical
predictions.
