  We use a probabilistic approach to study the rate of convergence to
equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger
than 2. The use of a coupling between two stochastic processes allows us to
extend and refine, in total variation distance, the polynomial rate of
convergence given in [AG11] and [KLT13]. This is, to our knowledge, the first
quantitative result in collisionless kinetic theory in dimension equal to or
larger than 2 that does not require any symmetry of the domain, nor a
monokinetic regime. Our study is also more general in terms of reflection at
the boundary: we allow for rather general diffusive reflections and for a
specular reflection component.
