  In modeling the interior of cells by simulating a reaction-diffusion master
equation over a grid of compartments, one employs the assumption that the copy
numbers of various chemical species are small, discrete quantities. We show
that in this case, textbook expressions for the change in Gibbs free energy
accompanying a chemical reaction or diffusion between adjacent compartments
become inaccurate. We derive exact expressions for these free energy changes
under the assumption of discrete copy numbers and illustrate how these
expressions reduce to the textbook expressions under a series of successive
approximations leveraging the relative sizes of the stoichiometric coefficients
and the copy numbers of the solutes and solvent. Numerical results are
presented to corroborate the claim that if the copy numbers are treated as
discrete quantities, then only these more exact expressions lead to correct
equilibrium behavior. The newly derived expressions are critical for correctly
tracking dissipation and entropy production in mesoscopic simulations based on
the reaction-diffusion master equation formalism.
