We report the study of a random Lorentz gas with a reaction of isomerization $A\rightleftharpoons B$ between two colors of moving particles elastically bouncing on hard disks. The reaction occurs when the moving particles collide on catalytic disks, which constitute a fraction of all the disks. Under dilute-gas conditions, the reaction-diffusion process is ruled by two coupled Boltzmann-Lorentz equations for the distribution functions of the colors. The macroscopic reaction-diffusion equations with cross-diffusion terms induced by the chemical reaction are derived from the kinetic equations. We use an $H$ theorem of the kinetic theory in order to derive a macroscopic entropy depending on the gradients of color densities and which has a non-negative entropy production in agreement with the second law of thermodynamics.

• Received 17 November 2004

DOI:https://doi.org/10.1103/PhysRevE.71.036147