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Entropy 2015, 17(4), 2184-2197; doi:10.3390/e17042184

Implications of Non-Differentiable Entropy on a Space-Time Manifold

1
Department of Physics, Gheorghe Asachi Technical University of Iaşi, Carol I Blv. 11, Iaşi 700050,România
2
Faculty of Mathematics, "Al. I. Cuza" University, Carol I Bd. 11, Iaşi 700506, România
3
Faculty of Agriculture, Agroeconomy Department, University of Agricultural Sciences and Veterinary Medicine Iaşi, Mihail Sadoveanu Alley 3, Iaşi 700490, România
4
Origyn Fertility Center, Clinical Hospital of Obstetrics and Gynaecology, Grigore T. Popa University of Medicine and Pharmacy, Iaşi 700032, Romania
*
Authors to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Received: 14 February 2015 / Revised: 7 April 2015 / Accepted: 7 April 2015 / Published: 13 April 2015
(This article belongs to the Section Complexity)
View Full-Text   |   Download PDF [242 KB, uploaded 13 April 2015]

Abstract

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-time manifold in the hydrodynamic version and its correspondence with motion variables (energy, momentum, etc.) are established. Moreover, for the same non-differentiability type, through a scale resolution dependence of a fundamental length and wave function independence with respect to the proper time, a non-differentiable Klein–Gordon-type equation in the wave function version is obtained. For a phase-amplitude functional dependence on the wave function, the non-differentiable spontaneous symmetry breaking mechanism implies pattern generation in the form of Cooper non-differentiable-type pairs, while its non-differentiable topology implies some fractal logic elements (fractal bit, fractal gates, etc.). View Full-Text
Keywords: non-differentiable entropy; fractal bit; space-time manifold; space-time scale relativity theory non-differentiable entropy; fractal bit; space-time manifold; space-time scale relativity theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Agop, M.; Gavriluţ, A.; Ştefan, G.; Doroftei, B. Implications of Non-Differentiable Entropy on a Space-Time Manifold. Entropy 2015, 17, 2184-2197.

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