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Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

1
Department of Physics, Gheorghe Asachi Technical University of Iași, Bd. D. Mangeron, no.67, Iași, 700050, Romania
2
Faculty of Mathematics, "Al. I. Cuza" University, Carol I Bd. 11, Iași, 700506, Romania
3
Psychiatry, Psychotherapy and Counseling Center Iași, Iași, 700115, Romania
4
Origyn Fertility Center, Clinical Hospital of Obstetrics and Gynaecology, "Grigore T. Popa" University of Medicine and Pharmacy, Iași, 700115, Romania
*
Author to whom correspondence should be addressed.
Entropy 2014, 16(11), 6042-6058; https://doi.org/10.3390/e16116042
Received: 17 July 2014 / Revised: 9 November 2014 / Accepted: 12 November 2014 / Published: 18 November 2014
(This article belongs to the Section Information Theory, Probability and Statistics)
Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are introduced. First of all, the dynamics equations of the complex system entities (Schrödinger-type or fractal hydrodynamic-type) are obtained. The last one gives a specific fractal potential, which generates uncertainty relations through non-differentiable entropy. Next, the correlation between informational non-differentiable entropy and informational non-differentiable energy implies specific uncertainty relations through a maximization principle of the informational non-differentiable entropy and for a constant value of the informational non-differentiable energy. Finally, for a harmonic oscillator, the constant value of the informational non-differentiable energy is equivalent to a quantification condition. View Full-Text
Keywords: non-differentiable entropy; informational non-differentiable entropy; informational non-differentiable energy; uncertainty relations non-differentiable entropy; informational non-differentiable entropy; informational non-differentiable energy; uncertainty relations
MDPI and ACS Style

Agop, M.; Gavriluț, A.; Crumpei, G.; Doroftei, B. Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems. Entropy 2014, 16, 6042-6058.

AMA Style

Agop M, Gavriluț A, Crumpei G, Doroftei B. Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems. Entropy. 2014; 16(11):6042-6058.

Chicago/Turabian Style

Agop, Maricel; Gavriluț, Alina; Crumpei, Gabriel; Doroftei, Bogdan. 2014. "Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems" Entropy 16, no. 11: 6042-6058.

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