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Entropy production in diffusion-reaction systems: The reactive random Lorentz gas

Laszlo Matyas·Pierre Gaspard
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Abstract

We report the study of a random Lorentz gas with a reaction of isomerization $A\rightleftharpoons B$ between the 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 the 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 a $H$-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.

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Laszlo Matyas, Pierre Gaspard. 2004-11-30. Entropy production in diffusion-reaction systems: The reactive random Lorentz gas. https://doi.org/10.1103/physreve.71.036147

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