  Under the assumption of a smooth full phase-space distribution function we
prove that the nonequilibrium entropy S which is considered as a functional of
the distribution vector for an N-body system possesses a lower bound and
therefore can not decrease. We also compute the rate of change of S, dS/dt,
showing that this is non-negative and having a global minimum at equilibrium.
As an aplication we obtain a generalization of the (Bhatnager-Gross-Krook) BGK
relaxation model.
