- 11-77 A.N. Gorban, G.S. Yablonsky
- Extended Detailed Balance for Systems with Irreversible Reactions
May 20, 11
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Abstract. The principle of detailed balance states that in equilibrium
each elementary process is equilibrated by its reverse process.
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. In this case, the
principle of detailed balance cannot be applied directly. We
represent irreversible reactions as limits of reversible steps
and obtain the principle of detailed balance for complex
mechanisms with some irreversible elementary processes. We
proved two consequences of the detailed balance for these
mechanisms: the structural condition and the algebraic
condition that form together the extended form of detailed
balance. The algebraic condition is the principle of
detailed balance for the reversible part. The structural
condition is: 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
reaction. Physically, this means that the irreversible
reactions cannot be included in oriented pathways.
The systems with the extended form of detailed balance are also
the limits of the reversible systems with detailed balance when
some of the equilibrium concentrations (or activities) tend to
zero. Surprisingly, the structure of the limit reaction
mechanism crucially depends on the relative speeds of this
tendency to zero.