The second law of thermodynamics and multifractal distribution functions: Bin counting, pair correlations, and the Kaplan-Yorke conjecture

Autor(en)

William Graham Hoover, C G Hoover, Harald Posch, J. A. Codelli

Abstrakt

We explore and compare numerical methods for the determination of multifractal dimensions for a doubly-thermostatted harmonic oscillator. The equations of motion are continuous and time-reversible. At equilibrium the distribution is a four-dimensional Gaussian, so that all the dimension calculations can be carried out analytically. Away from equilibrium the distribution is a surprisingly isotropic multifractal strange attractor, with the various fractal dimensionalities in the range 1 < D < 4. The attractor is relatively homogeneous, with projected two-dimensional information and correlation dimensions which are nearly independent of direction. Our data indicate that the Kaplan–Yorke conjecture (for the information dimension) fails in the full four-dimensional phase space. We also find no plausible extension of this conjecture to the projected fractal dimensions of the oscillator. The projected growth rate associated with the largest Lyapunov exponent is negative in the one-dimensional coordinate space.

Organisation(en)

Computergestützte Physik und Physik der Weichen Materie

Externe Organisation(en)

University of California, Davis

Journal

Communications in Nonlinear Science and Numerical Simulation

Band

12

Seiten

214-231

Anzahl der Seiten

18

ISSN

1007-5704

DOI

https://doi.org/10.1016/j.cnsns.2005.02.002

Publikationsdatum

2007

Peer-reviewed

Ja

ÖFOS 2012

103008 Experimentalphysik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/89fc2f69-f4bb-45fc-bedb-9229216cce99