Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

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.

DOI: 10.3390/e16116042

Extracted Key Phrases

Cite this paper

@article{Agop2014InformationalNE, title={Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems}, author={Maricel Agop and Alina Gavrilut and Gabriel Crumpei and Bogdan Doroftei}, journal={Entropy}, year={2014}, volume={16}, pages={6042-6058} }