Extremal Principles of Thermodynamics in an Exactly Solvable Rayleigh Gas Model

Extremal principles of irreversible thermodynamics are considered, such as the principles of minimum and maximum entropy production in an analytically exactly solvable model of a Rayleigh gas with and without particle sources. It is shown that in an isolated system, during relaxation to an equilibrium state, the entropy production is minimal. In a system with sources, during relaxation of an equilibrium state to a nonequilibrium state, the entropy production is maximum. The concepts of free and forced the relaxation are introduced. Free relaxation is the transition of a system from a state far from equilibrium to a state close to equilibrium. Moreover, at each moment of relaxation, entropy production is minimal, i.e. the principle of minimum entropy production is fulfilled. During forced relaxation, the system moves from a state close to equilibrium to a state far from equilibrium, in which case the entropy production is maximum. It is shown that the principles of minimum and maximum entropy production are variational principles of irreversible thermodynamics under various thermodynamic conditions.