2008/05/03 by Sergey G. Abaimov, S. G. Abaimov, Abaimov, S. G.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Mathematical Dynamics and Fractals #Statistical Mechanics and Entropy #nlin.CD
paper · pdf · doi:10.48550/arxiv.0805.0347
arxiv created 2008/05/03 · arxiv updated 2009/12/01
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.