### 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) |
---|---|

Pages (from-to) | 1089-1103 |

Number of pages | 15 |

Journal | Journal of Statistical Physics |

Volume | 146 |

Issue number | 5 |

DOIs | |

State | Published - Mar 2012 |

### Fingerprint

### Keywords

- Energy profiles
- Invariant measures
- Mechanical chains

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

**Nonequilibrium Steady States of Some Simple 1-D Mechanical Chains.** / Ryals, Brian; Young, Lai-Sang.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 146, no. 5, pp. 1089-1103. https://doi.org/10.1007/s10955-012-0437-6

}

TY - JOUR

T1 - Nonequilibrium Steady States of Some Simple 1-D Mechanical Chains

AU - Ryals, Brian

AU - Young, Lai-Sang

PY - 2012/3

Y1 - 2012/3

N2 - 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.

AB - 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.

KW - Energy profiles

KW - Invariant measures

KW - Mechanical chains

UR - http://www.scopus.com/inward/record.url?scp=84857923804&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857923804&partnerID=8YFLogxK

U2 - 10.1007/s10955-012-0437-6

DO - 10.1007/s10955-012-0437-6

M3 - Article

AN - SCOPUS:84857923804

VL - 146

SP - 1089

EP - 1103

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -