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In modeling the interior of cells by simulating a reaction-diffusion masterequation over a grid of compartments, one employs the assumption that the copynumbers of various chemical species are small, discrete quantities. We showthat in this case, textbook expressions for the change in Gibbs free energyaccompanying a chemical reaction or diffusion between adjacent compartmentsbecome inaccurate. We derive exact expressions for these free energy changesunder the assumption of discrete copy numbers and illustrate how theseexpressions reduce to the textbook expressions under a series of successiveapproximations leveraging the relative sizes of the stoichiometric coefficientsand the copy numbers of the solutes and solvent. Numerical results arepresented to corroborate the claim that if the copy numbers are treated asdiscrete quantities, then only these more exact expressions lead to correctequilibrium behavior. The newly derived expressions are critical for correctlytracking dissipation and entropy production in mesoscopic simulations based onthe reaction-diffusion master equation formalism.

A Discrete Approximation to Gibbs Free Energy of Chemical Reactions is  Needed for Accurately Calculating Entropy Production in Mesoscopic  Simulations