Chemical reactions that involve multiple, interconnected potential wells are of paramount importance in applications of chemical kinetics, particularly combustion and atmospheric chemistry. The only accurate way of determining phenomenological rate constants theoretically for this type of reaction is from the solution of a time-dependent, multiple-well master equation. In this Perspective we address the issue of whether or not (and to what extent) detailed balance is satisfied by rate constants obtained from such solutions. In addressing this issue we discuss a number of related topics, including necessary and sufficient conditions for a system of first-order rate equations to evolve to chemical equilibrium and the relationship between detailed balance and Wegscheider conditions. The assumption of a “near-Boltzmann” distribution in the wells sheds considerable light on the issue at hand. We discuss this approximation in some detail and suggest a quantitative measure of “near-Boltzmann”. It is extremely unlikely that the rate constants of interest satisfy detailed balance exactly (there is no reason to believe that they do). However, the discrepancies are expected to be vanishingly small, as observed in practice.

Detailed balance in multiple-well chemical reactions

Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special cases, both for the original models and the transformed ones.

R. K. Boyd

Papers

Detailed balance in nonequilibrium theories of chemical kinetics