Approach to equilibrium of coupled harmonic oscillator systems. II
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 atx 0 =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.
Key wordsEntropy information theory approach to equilibrium coupled oscillators Liouville function nonequilibrium statistical mechanics noncanonicale quilibrium harmonic chain
Unable to display preview. Download preview PDF.
- 1.M. A. Huerta and H. S. Robertson,J. Stat. Phys. 1:393 (1969).Google Scholar
- 2.H. S. Robertson and M. A. Huerta,Am. J. Phys. 38:619 (1970).Google Scholar
- 3.E. Schrödinger,Ann. Phys. 44:916 (1914).Google Scholar
- 4.M. A. Huerta, “Approach to Equilibrium of Infinite Chains of Coupled Harmonic Oscillators,” Thesis, Miami (1969); MIAPH-TP-69.24.Google Scholar
- 5.P. C. Hemmer, “Dynamic and Stochastic Types of Motion in the Linear Chain,” Thesis, Trondheim, Norway (1959).Google Scholar
- 6.J. M. Blatt,Progr. Theoret. Phys. 22:745 (1959).Google Scholar