The formulation of Prigogine's theorem is: In a stationary state, the production of entropy inside a thermodynamic system with constant external parameters is minimal and constant.
If the system is not in a stationary state, then it will change until the entropy production rate, or, in other words, the dissipative function of the system, takes the smallest value.According to this theorem, the stationary state of a linear non-equilibrium system (under conditions that prevent the achievement of an equilibrium state) corresponds to the minimum entropy production.
[2] Prigogine's theorem is valid if the kinetic coefficients in the Onsager relations are constant (do not depend on driving forces and flows); for real systems, it is valid only approximately, so the minimum entropy production for a stationary state is not such a general principle as the maximum entropy for an equilibrium state.
It has been experimentally established that Onsager's linear relations are valid in a fairly wide range of parameters for heat conduction and diffusion processes (for example, Fourier's law, Fick's law).
The principle is also violated for systems odd with respect to time reversal.