## 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) |
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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 |

## Keywords

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

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics