Extremums of Entropy Production and Second Law in Rayleigh Gas
  From the previously obtained solutions of the Fokker - Planck equation for Rayleigh gas (small impurity of heavy particles in a thermostat of light particles) with sources and without them, the entropy production was calculated. In a system without source (isolated system) shown that it holds theorem of Prigogine, and in a system with sources (open system) implementation of the principle of Ziegler (MEPP) depends on the relaxation direction. In an open system entropy production is compensate by a negative production of entropy, i.e. by a negentropy production. The algebraic sum of entropy and negentropy productions is called the generalized entropy production. From the balance of entropy and negentropy productions in an open system formulated a possible variation of the second law for open systems in a form: "At the relaxation of an open system to a nonequilibrium steady state, a generalized entropy production decreases in absolute value and equal to zero in a nonequilibrium steady state." Keywords: Fokker-Planck equation, Prigogine theorem, principle of maximum entropy production, the second law, negentropy. 
P. A. Tadjibaev and D. P. Tadjibaev
cond-mat.stat-mech