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arXiv · 1312.4301

Propagation of chaos for the thermostatted Kac master equation

Eric Carlen·Dawan Mustafa·Bernt Wennberg
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Abstract

The Kac model is a simplified model of an $N$-particle system in which the collisions of a real particle system are modeled by random jumps of pairs of particle velocities. Kac proved propagation of chaos for this model, and hence provided a rigorous validation of the corresponding Boltzmann equation. Starting with the same model we consider an $N$-particle system in which the particles are accelerated between the jumps by a constant uniform force field which conserves the total energy of the system. We show propagation of chaos for this model.

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Eric Carlen, Dawan Mustafa, Bernt Wennberg. 2014-07-21. Propagation of chaos for the thermostatted Kac master equation. https://doi.org/10.1007/s10955-014-1155-z

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