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Cited by 23,465

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Canonical dynamics: Equilibrium phase-space distributions

Hoover, William G.·1985·Physical Review A
DOI 10.1103/physreva.31.1695
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Abstract

Nos\'e 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 ${V}^{1/D}$ in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta ${p}_{s}$ and ${p}_{v}$. 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, ${p}_{x}$, V, \ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{}, and \ensuremath{\zeta}, where the x are reduced distances and the two variables \ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{} and \ensuremath{\zeta} 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.

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Research works printed but not linked: 11

  1. W. T. Ashurst, 1973, Phys. Rev. Lett., 31, 206, 10.1103/PhysRevLett.31.206 · DOI
  2. L. V. Woodcock, 1971, Chem. Phys. Lett., 10, 257, 10.1016/0009-2614(71)80281-6 · DOI
  3. D. J. Evans, 1983, J. Chem. Phys., 78, 3297, 10.1063/1.445195 · DOI
  4. W. G. Hoover, 1982, Phys. Rev. Lett., 48, 1818, 10.1103/PhysRevLett.48.1818 · DOI · Paper page
  5. J. M. Haile, 1983, J. Chem. Phys., 79, 3067, 10.1063/1.446137 · DOI
  6. H. J. C. Berendsen, 1984, J. Chem. Phys., 81, 3684, 10.1063/1.448118 · DOI · Paper page
  7. 1883, Philos. Mag., 15, 229, 10.1080/14786448308627342 · DOI
  8. H. C. Andersen, 1980, J. Chem. Phys., 72, 2384, 10.1063/1.439486 · DOI
  9. S. Nosé, 1984, Mol. Phys., 52, 255, 10.1080/00268978400101201 · DOI · Paper page
  10. M. Parrinello, 1983, Phys. Rev. Lett., 50, 1073, 10.1103/PhysRevLett.50.1073 · DOI · Paper page
  11. S. Nosé, 1984, J. Chem. Phys., 81, 511, 10.1063/1.447334 · DOI · Paper page

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Metadata

Authors
Hoover, W. G.
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
1985-03-01
Volume
31
Issue
3
Pages
1695-1697
ISSN
0556-2791 (ISSN-L)
DOI
10.1103/physreva.31.1695
OpenAlex
W1991794210
Cited by
23,465
References
0
FWCI
16.43
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)

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