### 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 | |

State | Published - Jan 1 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

- Kinetic equation with a thermostat
- Master equation
- Propagation of chaos

### Cite this

*Journal of Statistical Physics*,

*158*(6), 1341-1378. https://doi.org/10.1007/s10955-014-1155-z

}

*Journal of Statistical Physics*, vol. 158, no. 6, pp. 1341-1378. https://doi.org/10.1007/s10955-014-1155-z

**Propagation of Chaos for the Thermostatted Kac Master Equation.** / Carlen, Eric; Mustafa, Dawan; Wennberg, Bernt.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Propagation of Chaos for the Thermostatted Kac Master Equation

AU - Carlen, Eric

AU - Mustafa, Dawan

AU - Wennberg, Bernt

PY - 2015/1/1

Y1 - 2015/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=84925487975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925487975&partnerID=8YFLogxK

U2 - 10.1007/s10955-014-1155-z

DO - 10.1007/s10955-014-1155-z

M3 - Article

VL - 158

SP - 1341

EP - 1378

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 6

ER -