The second law of thermodynamics and multifractal distribution functions: Bin counting, pair correlations, and the Kaplan-Yorke conjecture
- Author(s)
- William Graham Hoover, C G Hoover, Harald Posch, J. A. Codelli
- Abstract
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(s)
- Computational and Soft Matter Physics
- External organisation(s)
- University of California, Davis
- Journal
- Communications in Nonlinear Science and Numerical Simulation
- Volume
- 12
- Pages
- 214-231
- No. of pages
- 18
- ISSN
- 1007-5704
- DOI
- https://doi.org/10.1016/j.cnsns.2005.02.002
- Publication date
- 2007
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103008 Experimental physics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/89fc2f69-f4bb-45fc-bedb-9229216cce99