Canonical dynamics: Equilibrium phase-space distributions

William G. Hoover
Phys. Rev. A 31, 1695 – Published 1 March 1985
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Abstract

Nosé has modified Newtonian dynamics so as to reproduce both the canonical and the isothermal-isobaric probability densities in the phase space of an N-body system. He did this by scaling time (with s) and distance (with V1/D in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta ps and pv. Here we develop a slightly different set of equations, free of time scaling. We find the dynamical steady-state probability density in an extended phase space with variables x, px, V, ε̇, and ζ, where the x are reduced distances and the two variables ε̇ and ζ act as thermodynamic friction coefficients. We find that these friction coefficients have Gaussian distributions. From the distributions the extent of small-system non-Newtonian behavior can be estimated. We illustrate the dynamical equations by considering their application to the simplest possible case, a one-dimensional classical harmonic oscillator.

  • Received 18 September 1984

DOI:https://doi.org/10.1103/PhysRevA.31.1695

©1985 American Physical Society

Authors & Affiliations

William G. Hoover

  • Department of Applied Science, University of California at DavisLivermore, Livermore, California 94550

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Issue

Vol. 31, Iss. 3 — March 1985

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