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Relaxation to a Perpetually Pulsating Equilibrium

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Abstract

Paper in honour of Freeman Dyson on the occasion of his 80th birthday. NormalN-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2kT, but, when inter-particle forces are an inverse cubic repulsion together with a linear (simple harmonic) attraction, the system pulsates for ever. In spite of this pulsation in scale,r(t), other degrees of freedom relax to an ever-changing Maxwellian distribution. With a new time, τ, defined so thatr 2d/dt = d/dτ it is shown that the remaining degrees of freedom evolve with an unchanging reduced Hamiltonian. The distribution predicted by equilibrium statistical mechanics applied to the reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature pulsates liker -2. Numerical simulation with 1000 particles demonstrate a rapid relaxation to this pulsating equilibrium.

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Authors and Affiliations

  1. Institute of Advanced Study, Princeton, New Jersey, 08540, USAInstitute of Astronomy, The Observatories, Madingley Road, Cambridge CB3 0HA

    D. Lynden-Bell & R. M. Lynden-Bell

  2. Institute of Astronomy, The Observatories, Madingley Road, Cambridge, CB3, 0HA

    D. Lynden-Bell

Authors
  1. D. Lynden-Bell
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  2. R. M. Lynden-Bell
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Lynden-Bell, D., Lynden-Bell, R.M. Relaxation to a Perpetually Pulsating Equilibrium. Journal of Statistical Physics 117, 199–209 (2004). https://doi.org/10.1023/B:JOSS.0000044068.53435.eb

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  • DOI: https://doi.org/10.1023/B:JOSS.0000044068.53435.eb

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