Sometimes, the principle of detailed balance is formulated in the narrow sense, for chemical reactions only but in the history of physics it has the broader use : it was invented for collisions, used for emission and absorption of quanta, for transport processes and for many other phenomena.
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The principle of detailed balance for the generalized mass action law is : For given values k _ r there exists a positive equilibrium a _ i ^ { \ rm eq } > 0 that satisfies detailed balance, that is, w _ r ^ + = w _ r ^ -.
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"' Yablonsky theorem "'. " 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 ."
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