# Reversible Diffusion-Limited Reactions: "Chemical Equilibrium" State and the Law of Mass Action Revisited

Source: [Reversible Diffusion-Limited Reactions: "Chemical Equilibrium" State and the Law of Mass Action Revisited](<https://www.sota2.com/research/paper/68fa267f2c2a3760193ba8cf>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:25:08.020Z

Authors: R. Voituriez, M. Moreau, G. Oshanin

Published: 2004-03-23T14:14:30.000Z

## Abstract

The validity of two fundamental concepts of classical chemical kinetics - the notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined for reversible \\textit{diffusion-limited} reactions (DLR), as exemplified here by association/dissociation $A+A \\rightleftharpoons B$ reactions. We consider a general model of long-ranged reactions, such that any pair of $A$ particles, separated by distance $\\mu$, may react with probability $\\omega\_+(\\mu)$, and any $B$ may dissociate with probability $\\omega\_-(\\lambda)$ into a geminate pair of $A$s separated by distance $\\lambda$. Within an exact analytical approach, we show that the asymptotic state attained by reversible DLR at $t = \\infty$ is generally \\textit{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 \\text{only} in physically unrealistic case when $\\omega\_+(\\mu) \\equiv \\omega\_-(\\mu)$ for any value of $\\mu$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0403586>)

[PDF](<https://arxiv.org/pdf/cond-mat/0403586.pdf>)