Extended Detailed Balance for Systems with Irreversible Reactions

TL;DR

This paper extends the principle of detailed balance to complex systems with both reversible and irreversible reactions by representing irreversible reactions as limits of reversible steps, establishing structural and algebraic conditions for such mechanisms.

Contribution

It introduces the extended detailed balance principle for systems with irreversible reactions and proves the structural and algebraic conditions that characterize these mechanisms.

Findings

The extended detailed balance principle applies to systems with irreversible reactions.

Irreversible reactions cannot be part of oriented pathways under the structural condition.

The structure of the limit reaction mechanism depends on the relative speeds at which equilibrium concentrations tend to zero.

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.