Reversible diffusion-limited reactions: "Chemical Equilibrium" state and the Law of Mass Action revisited

Two fundamental notions of classical chemical kinetics - the "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined here for reversible diffusion-limited reactions (DLR), on the example of association/dissociation A + A → D reactions. We consider a general model with long-ranged elementary reaction rates, such that any pair of A particles, separated by distance μ, may react at a rate k₊(μ), and any B may dissociate at a rate k_- (λ) into a geminate pair of A's separated by distance λ. Within an exact analytical approach, we show that the state attained by reversible DLR at t = ∞ is generally not a true thermodynamic equilibrium, but rather a non-equilibrium steady state, and that the Law of Mass Action is invalid. The classical picture holds only in case when the ratio k₊(μ)/k_-(μ) is independent of μ for any μ.