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

Manuel A. Huerta, Harry S. Robertson

Research output: Contribution to journalArticle

26 Citations (Scopus)

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 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

Original languageEnglish (US)
Pages (from-to)393-414
Number of pages22
JournalJournal of Statistical Physics
Volume1
Issue number3
DOIs
StatePublished - Sep 1 1969

Fingerprint

information theory
Coupled Oscillators
Information Theory
Harmonic Oscillator
harmonic oscillators
Entropy
entropy
thermodynamics
Thermodynamics
Heat Bath
Canonical Ensemble
baths
Probability Density
momentum
heat
Phase Space
Momentum
Contact
Knowledge
Model

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

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

In: Journal of Statistical Physics, Vol. 1, No. 3, 01.09.1969, p. 393-414.

Research output: Contribution to journalArticle

@article{be50a0bf3b2b4d388653b3583a13a0cf,
title = "Entropy, information theory, and the approach to equilibrium of coupled harmonic oscillator systems",
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 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",
keywords = "approach to equilibrium, coupled harmonic oscillators, entropy, information theory, Liouville function, nonequilibrium statistical mechanics",
author = "Huerta, {Manuel A.} and Robertson, {Harry S.}",
year = "1969",
month = "9",
day = "1",
doi = "10.1007/BF01106579",
language = "English (US)",
volume = "1",
pages = "393--414",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "3",

}

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 -