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The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions): ''At equilibrium, each elementary process should be equilibrated by its reverse process.'' ==History== The principle of detailed balance was explicitly introduced for collisions by Ludwig Boltzmann. In 1872, he proved his H-theorem using this principle.〔Boltzmann, L. (1964), Lectures on gas theory, Berkeley, CA, USA: U. of California Press.〕 The arguments in favor of this property are founded upon microscopic reversibility.〔Tolman, R. C. (1938). ''The Principles of Statistical Mechanics''. Oxford University Press, London, UK.〕 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.〔Maxwell, J.C. (1867), (On the dynamical theory of gases ),'' Philosl Trans R Soc London,'' 157 , pp. 49–88〕 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.〔Einstein, A. (1916). Strahlungs-Emission und -Absorption nach der Quantentheorie (and absorption of radiation in quantum theory ), Verhandlungen der Deutschen Physikalischen Gesellschaft 18 (13/14). Braunschweig: Vieweg, 318–323. See also: A. Einstein (1917). Zur Quantentheorie der Strahlung (the quantum theory of radiation ), Physikalische Zeitschrift 18 (1917), 121–128. (English translation ): D. ter Haar (1967): The Old Quantum Theory. Pergamon Press, pp. 167–183.〕 In 1901, Rudolf Wegscheider introduced the principle of detailed balance for chemical kinetics.〔Wegscheider, R. (1901) (Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reactionskinetik homogener Systeme ), Monatshefte für Chemie / Chemical Monthly 32(8), 849–906.〕 In particular, he demonstrated that the irreversible cycles 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,〔Onsager, L. (1931), (Reciprocal relations in irreversible processes. ) I, Phys. Rev. 37, 405–426; II 38, 2265–2279〕 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.〔van Kampen, N.G. "Stochastic Processes in Physics and Chemistry", Elsevier Science (1992).〕〔Yablonskii, G.S., Bykov, V.I., Gorban, A.N., Elokhin, V.I. (1991), Kinetic Models of Catalytic Reactions, Amsterdam, The Netherlands: Elsevier.〕〔 Vol. 10 of the Course of Theoretical Physics(3rd Ed).〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「detailed balance」の詳細全文を読む スポンサード リンク
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