Inhomogeneous Boltzmann equations: Distance, asymptotics and comparison of the classical and quantum cases

► Kullback-Leibler distance is generalized for inhomogeneous case. ► The solution f of the Boltzmann equation, such that dist{M,f} is minimal, is found. ► Asymptotics and stability of solutions of the Boltzmann equations are studied. ► The results for boson, fermion and classical cases are compared.