Corrections to the law of mass action and properties of the asymptotic t=∞ state for reversible diffusion-limited reactions

For diffusion-limited reversible A+A⇌B reactions we reexamine two fundamental concepts of classical chemical kinetics - the notion of "chemical equilibrium" and the "law of mass action." We consider a general model with distance-dependent reaction rates, such that any pair of A particles, performing standard random walks on sites of a d-dimensional lattice and being at a distance μ apart of each other at time moment t, may associate forming a B particle at the rate k ₊(μ). In turn, any randomly moving B particle may spontaneously dissociate at the rate k _-(λ) into a geminate pair of As "born" at a distance λ apart of each other. Within a formally exact approach based on Gardiner's Poisson representation method we show that the asymptotic t=∞ state attained by such diffusion-limited reactions is generally not a true thermodynamic equilibrium, but rather a nonequilibrium steady state, and that the law of mass action is invalid. The classical concepts hold only in case when the ratio k ₊(μ)/k _-(μ) does not depend on μ for any μ.