Chapman-Enskog development of the multivariate master equation

C. Van den Broeck, J. Houard and M. Malek Mansour

Physica A: Statistical Mechanics and its Applications, 1980, vol. 101, issue 1, 167-184

Abstract: A systematic development for a Multivariate Master Equation (MME), describing reaction diffusion systems, is presented along the same lines as the Chapman-Enskog development of kinetic gas theory. Diffusion, which occurs at a very fast rate, brings the system near a state of diffusional equilibrium, the analogue of local equilibrium for gases. In diffusional equilibrium, the global Master Equation (ME) is shown to be an exact consequence of the MME. For finite systems, corrections to the global ME, resulting from the finiteness of the diffusion times, are calculated. The development is verified on an exactly solvable model and illustrated on the Schlögl model. The difficulties encountered in the thermodynamic limit are discussed, and possible outcomes suggested.

Date: 1980
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:101:y:1980:i:1:p:167-184

DOI: 10.1016/0378-4371(80)90107-7

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