### Abstract

The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled, harmonically bound oscillators is treated exactly, both when the initial description of the rest of the chain is canonical and when it is Gaussian. The necessary mathematical properties of the bound oscillator functions are developed and used to demonstrate exact equipartition of energy. The entropy of the finite segment, or system, is shown to evolve to a time-independent equilibrium state that is, in the limit of weak coupling, the correct one for a system of noninteracting harmonic oscillators.

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

Pages (from-to) | 2305-2311 |

Number of pages | 7 |

Journal | Journal of Mathematical Physics |

Volume | 12 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1971 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*12*(11), 2305-2311. https://doi.org/10.1063/1.1665536

**Exact equilibration of harmonically bound oscillator chains.** / Huerta, Manuel; Robertson, H. S.; Nearing, J. C.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 12, no. 11, pp. 2305-2311. https://doi.org/10.1063/1.1665536

}

TY - JOUR

T1 - Exact equilibration of harmonically bound oscillator chains

AU - Huerta, Manuel

AU - Robertson, H. S.

AU - Nearing, J. C.

PY - 1971/1/1

Y1 - 1971/1/1

N2 - The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled, harmonically bound oscillators is treated exactly, both when the initial description of the rest of the chain is canonical and when it is Gaussian. The necessary mathematical properties of the bound oscillator functions are developed and used to demonstrate exact equipartition of energy. The entropy of the finite segment, or system, is shown to evolve to a time-independent equilibrium state that is, in the limit of weak coupling, the correct one for a system of noninteracting harmonic oscillators.

AB - The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled, harmonically bound oscillators is treated exactly, both when the initial description of the rest of the chain is canonical and when it is Gaussian. The necessary mathematical properties of the bound oscillator functions are developed and used to demonstrate exact equipartition of energy. The entropy of the finite segment, or system, is shown to evolve to a time-independent equilibrium state that is, in the limit of weak coupling, the correct one for a system of noninteracting harmonic oscillators.

UR - http://www.scopus.com/inward/record.url?scp=36849098762&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849098762&partnerID=8YFLogxK

U2 - 10.1063/1.1665536

DO - 10.1063/1.1665536

M3 - Article

VL - 12

SP - 2305

EP - 2311

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

ER -