The second law of thermodynamics for open systems

By solving the Fokker–Planck equations, the distribution functions of heavy particles in a thermostat of light particles (Rayleigh gas) with and without external sources of heavy particles were previously obtained. From the obtained non-stationary distribution functions, having determined the entropy according to L. Boltzmann, analytical expressions for the production of entropy in open and isolated systems are found. The first introduced the concept of production of negentropy. The algebraic sum of the entropy and negentropy productions is defined as the generalized entropy production. It is shown that the sign of the generalized production of entropy determines the direction of relaxation of the open system, and the equality of the generalized production of entropy to zero ensures the balance of entropy and the stationarity of the state of the system. The second law of thermodynamics in open systems is formulated as, when an open system relaxes into a nonequilibrium stationary state, the generalized production of entropy decreases in absolute value and is equal to zero in a stationary nonequilibrium state.