### Abstract

Original language | English |
---|---|

Journal | Communications in Mathematical Physics |

Volume | 281 |

Issue number | 1 |

Pages (from-to) | 179-202 |

Number of pages | 24 |

ISSN | 0010-3616 |

DOIs | |

Publication status | Published - 2008 |

MoE publication type | A1 Journal article-refereed |

### Fields of Science

- 114 Physical sciences
- 111 Mathematics

### Cite this

*Communications in Mathematical Physics*,

*281*(1), 179-202. https://doi.org/10.1007/s00220-008-0480-y

}

*Communications in Mathematical Physics*, vol. 281, no. 1, pp. 179-202. https://doi.org/10.1007/s00220-008-0480-y

**Approach to equilibrium for the phonon Boltzmann equation.** / Bricmont, Jean; Kupiainen, Antti.

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

TY - JOUR

T1 - Approach to equilibrium for the phonon Boltzmann equation

AU - Bricmont, Jean

AU - Kupiainen, Antti

PY - 2008

Y1 - 2008

N2 - We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved quantities that diffuse to zero, and fast variables that are slaved to the slow ones. This slaving implies the Fourier law, which relates the induced currents to the gradients of the conserved quantities.

AB - We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved quantities that diffuse to zero, and fast variables that are slaved to the slow ones. This slaving implies the Fourier law, which relates the induced currents to the gradients of the conserved quantities.

KW - 114 Physical sciences

KW - 111 Mathematics

U2 - 10.1007/s00220-008-0480-y

DO - 10.1007/s00220-008-0480-y

M3 - Article

VL - 281

SP - 179

EP - 202

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -