### Abstract

We study nonequilibrium steady states of some 1-D mechanical models with N moving particles on a line segment connected to unequal heat baths. For a system in which particles move freely, exchanging energy as they collide with one another, we prove that the mean energy along the chain is constant and equal to, where T _{L} and T _{R} are the temperatures of the two baths. We then consider systems in which particles are trapped, i. e., each confined to its designated interval in the phase space, but these intervals overlap to permit interaction of neighbors. For these systems, we show numerically that the system has well defined local temperatures and obeys Fourier's Law (with energy-dependent conductivity) provided we vary the masses randomly to enable the repartitioning of energy. Dynamical systems issues that arise in this study are discussed though their resolution is beyond reach.

Original language | English (US) |
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Pages (from-to) | 1089-1103 |

Number of pages | 15 |

Journal | Journal of Statistical Physics |

Volume | 146 |

Issue number | 5 |

DOIs | |

State | Published - Mar 2012 |

### Keywords

- Energy profiles
- Invariant measures
- Mechanical chains

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Statistical Physics*,

*146*(5), 1089-1103. https://doi.org/10.1007/s10955-012-0437-6