Nonequilibrium Solutions of the Boltzmann Equation under the Action of an External Force

Abstract

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, nonequilibrium dampingless 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.