Prigogine's theorem is a theorem of
non-equilibrium thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an ex ...
, originally formulated by
Ilya Prigogine
Viscount Ilya Romanovich Prigogine (; ; 28 May 2003) was a Belgian physical chemist of Russian-Jewish origin, noted for his work on dissipative structures, complex systems, and irreversibility.
Prigogine's work most notably earned him the 19 ...
.
The formulation of Prigogine's theorem is:
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. If there are no such obstacles, then the production of entropy reaches its absolute minimum - zero. A linear system means the fulfillment of linear phenomenological relationships between
thermodynamic
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
flows and driving forces. The coefficients of proportionality in the relationships between flows and driving forces are called phenomenological coefficients.
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
Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distributes this kinetic energy ...
,
Fick's law
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second ...
). For chemical reactions, the linear assumption is valid in a narrow region near the state of
chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which both the Reagent, reactants and Product (chemistry), products are present in concentrations which have no further tendency to change with time, so that there is no observable chan ...
. The principle is also violated for systems odd with respect to time reversal.
References
External links
1977 Nobel Prize lecture by Ilya Prigogine
''Attribution note: early versions of this article were translated from the Russian-language Wikipedia article on this topic.''
Theorems
Thermodynamics
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