Propagation of Chaos for the Thermostatted Kac Master Equation

Eric Carlen; Dawan Mustafa; Bernt Wennberg

doi:10.1007/s10955-014-1155-z

Propagation of Chaos for the Thermostatted Kac Master Equation

Eric Carlen, Dawan Mustafa, Bernt Wennberg

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1341-1378
Number of pages	38
Journal	Journal of Statistical Physics
Volume	158
Issue number	6
DOIs	https://doi.org/10.1007/s10955-014-1155-z
State	Published - Mar 2015

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Kinetic equation with a thermostat
Master equation
Propagation of chaos

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10.1007/s10955-014-1155-z

Cite this

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title = "Propagation of Chaos for the Thermostatted Kac Master Equation",

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.",

keywords = "Kinetic equation with a thermostat, Master equation, Propagation of chaos",

author = "Eric Carlen and Dawan Mustafa and Bernt Wennberg",

note = "Funding Information: We would like to thank an anonymous referee for having read the previous version of this paper very carefully and for pointing out several important issues. E.C. would like to thank Chalmers Institute of Technology during a visit in the Spring of 2012, and would like to acknowledge support from N.S.F. Grant DMS-1201354. D.M. and B.W. would like to thank Kleber Carrapatoso for the discussions during the initial phase of this work. This work was supported by Grants from the Swedish Science Council and the Knut and Alice Wallenberg foundation. Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

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doi = "10.1007/s10955-014-1155-z",

language = "English (US)",

volume = "158",

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journal = "Journal of Statistical Physics",

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AU - Carlen, Eric

AU - Mustafa, Dawan

AU - Wennberg, Bernt

N1 - Funding Information: We would like to thank an anonymous referee for having read the previous version of this paper very carefully and for pointing out several important issues. E.C. would like to thank Chalmers Institute of Technology during a visit in the Spring of 2012, and would like to acknowledge support from N.S.F. Grant DMS-1201354. D.M. and B.W. would like to thank Kleber Carrapatoso for the discussions during the initial phase of this work. This work was supported by Grants from the Swedish Science Council and the Knut and Alice Wallenberg foundation. Publisher Copyright: © 2014, Springer Science+Business Media New York.

PY - 2015/3

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N2 - 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.

AB - 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.

KW - Kinetic equation with a thermostat

KW - Master equation

KW - Propagation of chaos

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Propagation of Chaos for the Thermostatted Kac Master Equation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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