Nonequilibrium entropy. Characterization of stationary states

A generalization of the Gibbs entropy postulate is proposed based on the BBGKY [Born-Bogoliubov-Green-Kirkwood-Yvon] hierarchy as the nonequilibrium entropy for a system of N interacting particles. By using this entropy and the methods of nonequilibrium thermodynamics, a master equation for the evolution of the distribution vector is derived. In addition, after neglecting correlations in this master equation the Boltzmann equation is obtained. Moreover, our theory enables us to characterize the nonequilibrium stationary states as the states of constant entropy avoiding divergences in the entropy. Nonequilibrium Green-Kubo type relations are also derived.