### Abstract

Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function ρ for the infinite chain is reduced by integrating over the "outside" variables to a function ρ_{N} of the variables of the N-particle segment that is the thermodynamic system. The reduced Liouville function ρ_{N} which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta at t = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of ρ_{N} measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As |t

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

Pages (from-to) | 393-414 |

Number of pages | 22 |

Journal | Journal of Statistical Physics |

Volume | 1 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1969 |

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### Keywords

- approach to equilibrium
- coupled harmonic oscillators
- entropy
- information theory
- Liouville function
- nonequilibrium statistical mechanics

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*1*(3), 393-414. https://doi.org/10.1007/BF01106579

**Entropy, information theory, and the approach to equilibrium of coupled harmonic oscillator systems.** / Huerta, Manuel A.; Robertson, Harry S.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 1, no. 3, pp. 393-414. https://doi.org/10.1007/BF01106579

}

TY - JOUR

T1 - Entropy, information theory, and the approach to equilibrium of coupled harmonic oscillator systems

AU - Huerta, Manuel A.

AU - Robertson, Harry S.

PY - 1969/9/1

Y1 - 1969/9/1

N2 - Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function ρ for the infinite chain is reduced by integrating over the "outside" variables to a function ρN of the variables of the N-particle segment that is the thermodynamic system. The reduced Liouville function ρN which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta at t = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of ρN measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As |t

AB - Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function ρ for the infinite chain is reduced by integrating over the "outside" variables to a function ρN of the variables of the N-particle segment that is the thermodynamic system. The reduced Liouville function ρN which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta at t = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of ρN measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As |t

KW - approach to equilibrium

KW - coupled harmonic oscillators

KW - entropy

KW - information theory

KW - Liouville function

KW - nonequilibrium statistical mechanics

UR - http://www.scopus.com/inward/record.url?scp=0011519626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011519626&partnerID=8YFLogxK

U2 - 10.1007/BF01106579

DO - 10.1007/BF01106579

M3 - Article

AN - SCOPUS:0011519626

VL - 1

SP - 393

EP - 414

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3

ER -