Принцип детального баланса в кинетических системах

Principle in kinetic systems
The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions). It states that at equilibrium, each elementary process is in equilibrium with its reverse process.

The principle of detailed balance was explicitly introduced for collisions by Ludwig Boltzmann. In 1872, he proved his H theorem using this principle. The arguments in favor of this property are founded upon microscopic reversibility. Five years before Boltzmann, James Clerk Maxwell used the principle of detailed balance for gas kinetics with the reference to the principle of sufficient reason. He compared the idea of detailed balance with other types of balancing (like cyclic balance) and found that "Now it is impossible to assign a reason" why detailed balance should be rejected (pg. 64). Albert Einstein in 1916 used the principle of detailed balance in a background for his quantum theory of emission and absorption of radiation. In 1901, Rudolf Wegscheider introduced the principle of detailed balance for chemical kinetics. In particular, he demonstrated that the irreversible cycles A1 > A2 > \cdots > A \mathit{n} > A1 are impossible and found explicitly the relations between kinetic constants that follow from the principle of detailed balance. In 1931, Lars Onsager used these relations in his works, for which he was awarded the 1968 Nobel Prize in Chemistry. The principle of detailed balance has been used in Markov chain Monte Carlo methods since their invention in 1953. In particular, in the Metropolis–Hastings algorithm and in its important particular case, Gibbs sampling, it is used as a simple and reliable condition to provide the desirable equilibrium state. Now, the principle of detailed balance is a standard part of the university courses in statistical mechanics, physical chemistry, chemical and physical kinetics.

For many systems of physical and chemical kinetics, detailed balance provides sufficient conditions for the strict increase of entropy in isolated systems. For example, the famous Boltzmann H theorem and generalized mass action kinetics with detailed balance. Nevertheless, the principle of detailed balance is not necessary for entropy growth. For example, in the linear irreversible cycle A1 > A2 > A3 > A1, entropy production is positive but the principle of detailed balance does not hold. Thus, the principle of detailed balance is a sufficient but not necessary condition for entropy increase in Boltzmann kinetics. These relations between the principle of detailed balance and the second law of thermodynamics were clarified in 1887 when Hendrik Lorentz objected to the Boltzmann H theorem for polyatomic gases. Lorentz stated that the principle of detailed balance is not applicable to collisions of polyatomic molecules. Boltzmann immediately invented a new, more general condition sufficient for entropy growth. Boltzmann's condition holds for all Markov processes, irrespective of time reversibility. Later, entropy increase was proved for all Markov processes by a direct method. These theorems may be considered as simplifications of the Boltzmann result. Later, this condition was referred to as the "cyclic balance" condition (because it holds for irreversible cycles) or the "semi detailed balance" or the "complex balance". In 1981, Carlo Cercignani and Maria Lampis proved that the Lorentz arguments were wrong and the principle of detailed balance is valid for polyatomic molecules. Nevertheless, the extended semi detailed balance conditions invented by Boltzmann in this discussion remain the remarkable generalization of the detailed balance.