Measuring information growth in fractal phase space

Details Measuring information growth in fractal phase space Measuring information growth in fractal phase space

2003-05-22

arxiv.org/abs/cond-mat/0305540v4

Chaos, Solitons & Fractals, 21(2004)893

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 eps figure, TeX. Chaos, Solitons & Fractals (2004), in press

Scientific paper

We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness, at any scale, of the information calculation in fractal support, the incomplete normalization $\sum_ip_i^q=1$ is applied throughout the paper. It is shown that the information growth is nonadditive and is proportional to the trace-form $\sum_ip_i-\sum_ip_i^q$ so that it can be connected to several nonadditive entropies. This information growth can be extremized to give, for non-equilibrium systems, power law distributions of evolving stationary state which may be called ``maximum entropic evolution''.

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