Variational Principles of Thermodynamics in a Rayleigh Gas Model

Using an analytically solvable model of a Rayleigh gas as an example, variational principles of irreversible thermodynamics are proposed. These principles are formulated for both isolated (without sources) and open (with sources) systems. It is shown that in an isolated system, entropy production is minimal during relaxation to an equilibrium state. Thus, Prigogine's principle of minimum entropy production is satisfied in an isolated system. In an open system with sources, during relaxation from an equilibrium state to a nonequilibrium state, entropy production is maximal, in accordance with Ziegler's principle. The concepts of free and forced 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 satisfied. During forced relaxation, a system transitions from a state close to equilibrium to a state far from equilibrium, in which case entropy production is maximized. Thus, the variational principle of irreversible thermodynamics for isolated systems is the principle of minimum entropy production, and for open systems, it is the principle of maximum entropy production.

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