Approach to equilibrium of coupled harmonic oscillator systems. II

Manuel A. Huerta; Harry S. Robertson

doi:10.1007/BF01019849

Approach to equilibrium of coupled harmonic oscillator systems. II

Manuel A. Huerta, Harry S. Robertson

Physics

Research output: Contribution to journal › Article

10 Scopus citations

Abstract

The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled masses is studied in several variations. The chain is taken as completely free, or it is bound at x₀=0; ordinary coordinates and momenta or Schrödinger variables are used to treat the dynamics; and the inital distribution of heat-bath variables is chosen to be canonical or noncanonical. Equipartition of energy is found in all cases. Brownian drifts are obtained for the free chain with ordinary variables, but when this is excluded, the equilibrium entropy is found to be canonical and extensive when the initial heat bath is canonical, but less than canonical and slightly nonextensive when the initial heat bath is noncanonical. The modifications of the entropy do not contribute to the heat capacity of the system.

Original language	English (US)
Pages (from-to)	171-189
Number of pages	19
Journal	Journal of Statistical Physics
Volume	3
Issue number	2
DOIs	https://doi.org/10.1007/BF01019849
State	Published - Jun 1 1971

Keywords

Entropy
Liouville function
approach to equilibrium
coupled oscillators
harmonic chain
information theory
noncanonicale quilibrium
nonequilibrium statistical mechanics

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01019849

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Huerta, M. A., & Robertson, H. S. (1971). Approach to equilibrium of coupled harmonic oscillator systems. II. Journal of Statistical Physics, 3(2), 171-189. https://doi.org/10.1007/BF01019849

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abstract = "The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled masses is studied in several variations. The chain is taken as completely free, or it is bound at x0=0; ordinary coordinates and momenta or Schr{\"o}dinger variables are used to treat the dynamics; and the inital distribution of heat-bath variables is chosen to be canonical or noncanonical. Equipartition of energy is found in all cases. Brownian drifts are obtained for the free chain with ordinary variables, but when this is excluded, the equilibrium entropy is found to be canonical and extensive when the initial heat bath is canonical, but less than canonical and slightly nonextensive when the initial heat bath is noncanonical. The modifications of the entropy do not contribute to the heat capacity of the system.",

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