154 research outputs found
Measuring information growth in fractal phase space
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
is applied throughout the paper. It is shown that the
information growth is nonadditive and is proportional to the trace-form
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''.Comment: 10 pages, 1 eps figure, TeX. Chaos, Solitons & Fractals (2004), in
pres
On the generalized entropy pseudoadditivity for complex systems
We show that Abe's general pseudoadditivity for entropy prescribed by thermal
equilibrium in nonextensive systems holds not only for entropy, but also for
energy. The application of this general pseudoadditivity to Tsallis entropy
tells us that the factorization of the probability of a composite system into
product of the probabilities of the subsystems is just a consequence of the
existence of thermal equilibrium and not due to the independence of the
subsystems.Comment: 8 pages, no figure, RevTe
The heuristic power of the non integer differential operator in physics: From chaos to emergence, auto-organisations and holistic rules
© 2015 by Nova Science Publishers, Inc. All rights reserved. The use of fractional differential equations raises a paradox due to the non-respect of the space time noetherian axioms. In environments characterized by scaling laws (hyperbolicgeometry associated with fractional diff integral) energy is no more the invariant of the dynamics. Nevertheless the experimental action requiringthe use of energy, the relevant representation of the fractional process, must be extended. The extension is carried out usingthe canonical transfer functions in Fourier space and explained by their links with the Riemann zeta function. Category theory informs the extension problem.Ultimately the extension can be expressed by asimple change of referential. It leads to embed the time in the complex space. This change unveils the presenceof a time singularity at infinity.The paradox of the energy in the fractality illuminates the heuristic power of thefractional differential equations. In this mathematical frame, it is shown that the dual requirement of the frequency response to differential equations of non-integer order and of the notherian constraints make gushing out a source of negentropique likely to formalize the emergence of macroscopic correlations into self-organized structures as well as holistic rules of behaviour
Electromagnetic field of fractal distribution of charged particles
Electric and magnetic fields of fractal distribution of charged particles are
considered. The fractional integrals are used to describe fractal distribution.
The fractional integrals are considered as approximations of integrals on
fractals. Using the fractional generalization of integral Maxwell equation, the
simple examples of the fields of homogeneous fractal distribution are
considered. The electric dipole and quadrupole moments for fractal distribution
are derived.Comment: RevTex, 21 pages, 2 picture
Possible Experimental Test of Continuous Medium Model for Fractal Media
We use the fractional integrals to describe fractal media. We consider the
fractal media as special ("fractional") continuous media. We discuss the
possible experimental testing of the continuous medium model for fractal media
that is suggested in Phys. Lett. A. 336 (2005) 167-174. This test is connected
with measure of period of the Maxwell pendulum with fractal medium cylinder.Comment: 9 page
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