Application of classical statistical mechanics to multifractals and dynamical systems

Details Application of classical statistical mechanics to multifractals and dynamical systems Application of classical statistical mechanics to multifractals and dynamical systems

2008-05-03

arxiv.org/abs/0805.0347v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

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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