Fluctuations in reversible chemical reactions

The paper proposes a new approach to describe fluctuations of reversible chemical reactions in closed systems. The deterministic rate laws are cast into the form of nonlinear Onsager type closed laws. By means of nonlinear transport theory a Fokker-Planck equation describing the stochastic process of concentration fluctuations is obtained. It is shown that the stochastic formulation reduces to the correct deterministic rate laws in the thermodynamic limit V → ∞ with the concentrations kept fixed. Concrete examples of reactions in ideal mixtures are given and the results of the presented approach are compared with those of the usual approach by means of a birth and death type master equation. It is shown that both approaches lead to the same stationary probability and exhibit the same natural boundaries reflecting the fact of a restricted state space. The proposed Fokker-Planck equation is different from the Fokker-Planck equation obtained from the master equation by truncating its Kramers-Moyal expansion. However, the two equations are shown to have identical Fokker-Planck coefficients in the vicinity of the deterministic equilibrium state. Compared with the usual master equation approach the proposed stochastic modeling of chemical reactions has the advantage of allowing for a straightforward extension to reactions in non-ideal mixtures.