Calculation of the Entropy Balance Equation in a Non-equilibrium Reaction-diffusion System

In this article, we discuss the relationships between thermodynamic quantities and the spatial pattern in a reaction-diffusion model based on the reversible Gray-Scott model. This model is introduced for calculation of the entropy production in a reaction-diffusion system. First, we show the relationship between entropy production and pattern formation, and suggest that the entropy production could be an index of different patterns. Then the entropy production is applied for searching the parameter region where the pattern is bistable. Moreover, the entropy change is calculated by using the relative chemical potential that is defined based on the equilibrium state and not on the standard chemical potential. The results of the entropy change are consistent with the intrinsic property of the entropy, therefore, the entropy change calculated in this way may be regarded as an appropriate quantity for the discussion of the thermodynamic properties in a non equilibrium system.