88 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
About an alternative distribution function for fractional exclusion statistics
We show that it is possible to replace the actual implicit distribution
function of the fractional exclusion statistics by an explicit one whose form
does not change with the parameter . This alternative simpler
distribution function given by a generalization of Pauli exclusion principle
from the level of the maximal occupation number is not completely equivalent to
the distributions obtained from the level of state number counting of the
fractional exclusion particles. Our result shows that the two distributions are
equivalent for weakly bosonized fermions () at not very high
temperatures.Comment: 8 pages, 3 eps figures, TeX. Nuovo Cimento B (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
Maximum Path Information and Fokker-Planck Equation
We present in this paper a rigorous method to derive the nonlinear
Fokker-Planck (FP) equation of anomalous diffusion directly from a
generalization of the principle of least action of Maupertuis proposed by Wang
for smooth or quasi-smooth irregular dynamics evolving in Markovian process.
The FP equation obtained may take two different but equivalent forms. It was
also found that the diffusion constant may depend on both q (the index of
Tsallis entropy) and the time t.Comment: 7 page
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