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.
22.
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 ^ -.
23.
"' 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 ."
