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In 1901, R. Wegscheider introduced the principle of detailed balance for chemical kinetics.<ref>[http://dx.doi.org/10.1007/BF01517498 Rud Wegscheider "Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reactionskinetik homogener Systeme", Monatshefte für Chemie '''22''' pp. 849-906 (1901)]</ref> In particular, he demonstrated that the irreversible cycles <math>A_1 \to A_2 \to ... \to A_n \to A_1</math> are impossible and found explicitly the relations between kinetic constants that follow from the principle of detailed balance. | In 1901, R. Wegscheider introduced the principle of detailed balance for chemical kinetics.<ref>[http://dx.doi.org/10.1007/BF01517498 Rud Wegscheider "Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reactionskinetik homogener Systeme", Monatshefte für Chemie '''22''' pp. 849-906 (1901)]</ref> In particular, he demonstrated that the irreversible cycles <math>A_1 \to A_2 \to ... \to A_n \to A_1</math> are impossible and found explicitly the relations between kinetic constants that follow from the principle of detailed balance. | ||
See also <ref name=vanKampen1992>van Kampen, N.G. "Stochastic Processes in Physics and Chemistry", Elsevier Science (1992).</ref> | |||
<ref>Lifshitz, E.M., Pitaevskii, L.P., Physical kinetics (1981)London: Pergamon. Vol. 10 of the Course of Theoretical Physics(3rd Ed).</ref> | |||
==Microscopic background== | ==Microscopic background== | ||
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== Detailed balance for systems with irreversible reactions == | == Detailed balance for systems with irreversible reactions == | ||
Detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process and required reversibility of all elementary processes. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc), detailed mechanisms include both reversible and irreversible reactions. If one represents irreversible reactions as limits of reversible steps, then it become obvious that not all reaction mechanisms with irreversible reactions can be obtained as limits of systems or reversible reactions with detailed balance. For example, the irreversible cycle <math>A_1 \to A_2 \to A_3 \to A_1</math> cannot be obtained as such a limit but the reaction mechanism <math>A_1 \to A_2 \to A_3 \leftarrow A_1</math> can <ref> | Detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process and required reversibility of all elementary processes. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc), detailed mechanisms include both reversible and irreversible reactions. If one represents irreversible reactions as limits of reversible steps, then it become obvious that not all reaction mechanisms with irreversible reactions can be obtained as limits of systems or reversible reactions with detailed balance. For example, the irreversible cycle <math>A_1 \to A_2 \to A_3 \to A_1</math> cannot be obtained as such a limit but the reaction mechanism <math>A_1 \to A_2 \to A_3 \leftarrow A_1</math> can.<ref>Chu, Ch. (1971), Gas absorption accompanied by a system of first-order reactions, Chem. Eng. Sci. 26(3), 305-312.</ref> | ||
''A system of reactions with some irreversible reactions is a limit of systems with detailed balance when some constants tend to zero if and only if (i) the reversible part of this system satisfies the principle of detailed balance and (ii) the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reactions.''<ref name=GorbanYablonsky2011/> Physically, the last condition means that the irreversible reactions cannot be included in oriented cyclic pathways. | ''A system of reactions with some irreversible reactions is a limit of systems with detailed balance when some constants tend to zero if and only if (i) the reversible part of this system satisfies the principle of detailed balance and (ii) the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reactions.''<ref name=GorbanYablonsky2011/> Physically, the last condition means that the irreversible reactions cannot be included in oriented cyclic pathways. | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
'''Related reading''' | |||
*[http://en.wikipedia.org/wiki/Detailed_balance Detailed balance] in Wikipedia | |||
*[http://dx.doi.org/10.1063/1.477973 Vasilios I. Manousiouthakis and Michael W. Deem "Strict detailed balance is unnecessary in Monte Carlo simulation", Journal of Chemical Physics '''110''' pp. 2753- (1999)] | *[http://dx.doi.org/10.1063/1.477973 Vasilios I. Manousiouthakis and Michael W. Deem "Strict detailed balance is unnecessary in Monte Carlo simulation", Journal of Chemical Physics '''110''' pp. 2753- (1999)] | ||
[[category: statistical mechanics]] | [[category: statistical mechanics]] | ||
[[category: Non-equilibrium thermodynamics]] | [[category: Non-equilibrium thermodynamics]] |