Field theory of reaction-diffusion: Law of mass action with an energetic variational approach.

Phys Rev E

Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA and Department of Physiology and Biophysics, Rush University, 1750 W. Harrison, Chicago, Illinois 60612, USA.

Published: December 2020

We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by the choice of the free energy and the dynamics of the chemical reaction is determined by the choice of the dissipation. This approach enables us to couple chemical reactions with other effects, such as diffusion and drift in an electric field. As an illustration, we apply our approach to a nonequilibrium reaction-diffusion system in a specific but canonical setup. We show by numerical simulations that the input-output relation of such a system depends on the choice of the dissipation.

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http://dx.doi.org/10.1103/PhysRevE.102.062147DOI Listing

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