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Entropy 2014, 16(11), 6042-6058; doi:10.3390/e16116042

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.
Received: 17 July 2014 / Revised: 9 November 2014 / Accepted: 12 November 2014 / Published: 18 November 2014
(This article belongs to the Section Information Theory)
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Abstract

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

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