Application of classical statistical mechanics to multifractals and dynamical systems
Chaotic Dynamics
2008-05-06 v1
Abstract
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply similar formalism to non-Hamiltonian dynamical systems. Although these theories reveal aspects of complex behavior, they have limited applicability. This paper applies the classical Gibbs-Boltzmann statistical mechanics to complex systems such as i.i.d. processes, multifractals, and non-Hamiltonian dynamical systems with strange attractors. The effective thermolization of stochastic noise in the system is introduced and the formalism of a ruling (governing, free energy) potential is developed.
Cite
@article{arxiv.0805.0347,
title = {Application of classical statistical mechanics to multifractals and dynamical systems},
author = {S. G. Abaimov},
journal= {arXiv preprint arXiv:0805.0347},
year = {2008}
}