Three-variable reversible Gray–Scott model

Even though the field of nonequilibrium thermodynamics has been popular and its importance has been suggested by Demirel and Sandler [J. Phys. Chem. B 108, 31 (2004)], there are only a few investigations of reaction-diffusion systems from the aspect of thermodynamics. A possible reason is that model equations are complicated and difficult to analyze because the corresponding chemical reactions need to be reversible for thermodynamical calculations. Here, we introduce a simple model for calculation of entropy production rate: a three-variable reversible Gray-Scott model. The rate of entropy production in self-replicating pattern formation is calculated, and the results are compared with those reported based on the Brusselator model in the context of biological cell division.