Propagation of Chaos for a Thermostated Kinetic Model

Abstract

We consider a system of N point particles moving on a d-dimensional torus. Each particle is subject to a uniform field E and random speed conserving collisions. This model is a variant of the Drude-Lorentz model of electrical conduction. In order to avoid heating by the external field, the particles also interact with a Gaussian thermostat which keeps the total kinetic energy of the system constant. The thermostat induces a mean-field type of interaction between the particles. Here we prove that, starting from a product measure, in the large N limit, the one particle velocity distribution satisfies a self consistent Vlasov-Boltzmann equation.. This is a consequence of "propagation of chaos", which we also prove for this model.

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References in corpus (4)

• Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations
• Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system
• Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas
• Speed Distribution of N Particles in the Thermostated Periodic Lorentz Gas with a Field

Cited by in corpus (5)

• Uniform propagation of chaos for the thermostated Kac model
• Propagation of chaos for the thermostatted Kac master equation
• On a thermostated Kac model with rescaling
• Autonomous evolution of electron speeds in a thermostatted system: exact results
• Entropic Chaoticity for the Steady State of a Current Carrying System