The first term on the right hand side of the equation presents a stream of thermal energy into the system; the last term—a part of a stream of energy h_\alpha coming into the system with the stream of particles of substances \Delta N_\alpha that can be positive or negative, \eta_\alpha= h_\alpha- \mu_\alpha, where \mu_\alpha is chemical potential of substance \alpha. The middle term in (1) depicts energy dissipation (entropy production) due to the relaxation of internal variables \xi_j. In the case of chemically reacting substances, which was investigated by Prigogine, the internal variables appear to be measures of incompleteness of chemical reactions, that is measures of how much the considered system with chemical reactions is out of equilibrium. The theory can be generalised,Pokrovskii V.N. (2005) Extended thermodynamics in a discrete-system approach, Eur. J. Phys. vol. 26, 769-781. to consider any deviation from the equilibrium state as an internal variable, so that we consider the set of internal variables \xi_j in equation (1) to consist of the quantities defining not only degrees of completeness of all chemical reactions occurring in the system, but also the structure of the system, gradients of temperature, difference of concentrations of substances and so on.
