Intrinsic irreversibility and the validity of the kinetic description of chaotic systems

Journal Article · Thu Sep 01 04:00:00 EDT 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.50.1781· OSTI ID:7198071

Hasegawa, H H; Driebe, D J ^[1]

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1. Center for Studies in Statistical Mechanics and Complex Systems, University of Texas at Austin, Austin, Texas 78712 (United States) International Solvay Institutes for Physics and Chemistry, 1050 Brussels (Belgium)

Irreversibility for a class of chaotic systems is seen to be an exact consequence of the dynamics through the use of a generalized spectral representation of the time evolution operator of probability densities. The generalized representation is valid for one-dimensional systems when the initial probability density satisfies certain physical conditions'' of smoothness. The formalism is first applied to the one-dimensional multi-Bernoulli map, which is a simple map displaying deterministic diffusion. The two-dimensional, invertible baker and multibaker transformations are then studied and the physical conditions determining which discrete spectral values are realized are seen to depend on the smoothness of both the density as well as the observable considered. The generalized representation is constructed using a resolvent formalism. The eigenstates of the diffusive systems are seen to be of a fractal nature.

• DOE Contract Number: FG05-88ER13897
• OSTI ID: 7198071
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 50:3; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFUSION
EIGENSTATES
FRACTALS
IRREVERSIBLE PROCESSES
KINETICS
MAPPING
PROBABILITY
STOCHASTIC PROCESSES