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 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.
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References
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Supported in part by the United States Atomic Energy Commission.
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Huerta, M.A., Robertson, H.S. Approach to equilibrium of coupled harmonic oscillator systems. II. J Stat Phys 3, 171–189 (1971). https://doi.org/10.1007/BF01019849
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DOI: https://doi.org/10.1007/BF01019849