The theorem was proved by Prigogine in 1947 from the Onsager relations. 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). For chemical reactions, the linear assumption is valid in a narrow region near the state of chemical equilibrium. The principle is also violated for systems odd with respect to time reversal.