### Abstract

As a paradigm for heat conduction in 1 dimension, we propose a class of models represented by chains of identical cells, each one of which contains an energy storage device called a ''tank''. Energy exchange among tanks is mediated by tracer particles, which are injected at characteristic temperatures and rates from heat baths at the two ends of the chain. For stochastic and Hamiltonian models of this type, we develop a theory that allows one to derive rigorously - under physically natural assumptions - macroscopic equations for quantities related to heat transport, including mean energy profiles and tracer densities. Concrete examples are treated for illustration, and the validity of the Fourier Law in the present context is discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 237-267 |

Number of pages | 31 |

Journal | Communications in Mathematical Physics |

Volume | 262 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2006 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*262*(1), 237-267. https://doi.org/10.1007/s00220-005-1462-y

**Nonequilibrium energy profiles for a class of 1-D models.** / Eckmann, J. P.; Young, Lai-Sang.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 262, no. 1, pp. 237-267. https://doi.org/10.1007/s00220-005-1462-y

}

TY - JOUR

T1 - Nonequilibrium energy profiles for a class of 1-D models

AU - Eckmann, J. P.

AU - Young, Lai-Sang

PY - 2006/2

Y1 - 2006/2

N2 - As a paradigm for heat conduction in 1 dimension, we propose a class of models represented by chains of identical cells, each one of which contains an energy storage device called a ''tank''. Energy exchange among tanks is mediated by tracer particles, which are injected at characteristic temperatures and rates from heat baths at the two ends of the chain. For stochastic and Hamiltonian models of this type, we develop a theory that allows one to derive rigorously - under physically natural assumptions - macroscopic equations for quantities related to heat transport, including mean energy profiles and tracer densities. Concrete examples are treated for illustration, and the validity of the Fourier Law in the present context is discussed.

AB - As a paradigm for heat conduction in 1 dimension, we propose a class of models represented by chains of identical cells, each one of which contains an energy storage device called a ''tank''. Energy exchange among tanks is mediated by tracer particles, which are injected at characteristic temperatures and rates from heat baths at the two ends of the chain. For stochastic and Hamiltonian models of this type, we develop a theory that allows one to derive rigorously - under physically natural assumptions - macroscopic equations for quantities related to heat transport, including mean energy profiles and tracer densities. Concrete examples are treated for illustration, and the validity of the Fourier Law in the present context is discussed.

UR - http://www.scopus.com/inward/record.url?scp=29644442958&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29644442958&partnerID=8YFLogxK

U2 - 10.1007/s00220-005-1462-y

DO - 10.1007/s00220-005-1462-y

M3 - Article

VL - 262

SP - 237

EP - 267

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -