On the retarded solution of the Liouville equation and the definition of entropy in kinetic theory

Zubarevs approach to non-equilibrium statistical mechanics, which consists in adding a source term to the Liouville equation so as to select its retarded solution, is reinvestigated. As discussed earlier, the source has to be modified by introducing a different set of thermodynamic parameters in order to achieve agreement with current theories of non-equilibrium statistical mechanics. By considering kinetic theory of a homogeneous classical gas it is demonstrated that the modification of the source is necessary in order to avoid unphysical divergencies and to maintain conservation laws. Moreover, a new definition of the non-equilibrium entropy in terms of the relevant observables is obtained which reveals several attractive features.