Abstract
We consider a (deterministic, conservative) one-dimensional system of colored hard points, changing color each time they hit one another with a relative velocity above a threshold. In the limit of rare reactions, theN-particle color distribution follows a Markovian birth-and-death process. Using the reaction rate as an intrinsic time scale, we also obtain the reaction-diffusion equation for a test particle in this hydrodynamic limit. Explicit results are given for a discrete and a Maxwellian velocity distribution.
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Elskens, Y. Microscopic derivation of a Markovian Master equation in a deterministic model of chemical reaction. J Stat Phys 37, 673–695 (1984). https://doi.org/10.1007/BF01010501
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DOI: https://doi.org/10.1007/BF01010501