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arXiv · 0805.0347

Application of classical statistical mechanics to multifractals and dynamical systems

S. G. Abaimov
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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.

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S. G. Abaimov. 2008-05-03. Application of classical statistical mechanics to multifractals and dynamical systems. https://arxiv.org/abs/0805.0347

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