  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.
