Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

Agop, M.; Gavriluţ, Alina; Crumpei, Gabriel; Doroftei, Bogdan

doi:10.3390/e16116042

Cited by 14 publications

(27 citation statements)

References 35 publications

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“…It can be seen that such a pair "operates" in a state of maximum informational entropy (for details see [12,15]). However, our fractal model extends the potential domain of applications for Schrödinger-type equations to every system in which the three conditions (an infinite or very large number of trajectories, a fractal dimension of individual trajectories, local irreversibility) are fulfilled.…”

Section: Pairs Generating Mechanisms: Implications In Dynamics Of Biomentioning

confidence: 99%

“…In this framework, in Figure 1 we present the states density ρ = ΨΨ for this system, where Ψ is the complex conjugate of Ψ determined from Equation (9) for the stationary case, while in Figure 2 the associated informational entropy is shown. It can be seen that such a pair "operates" in a state of maximum informational entropy (for details see [12,15]). …”

Section: Pairs Generating Mechanisms: Implications In Dynamics Of Biomentioning

confidence: 99%

“…where λ is the fractal-nonfractal transition coefficient, considered with "+" for dω 0 and with "−" for dω 0 (for details see [10][11][12][15][16][17]) and δ il the Kronecker tensor, the fractal equation of the motion (geodesics equation) has the following form:…”

Section: Hallmarks Of Non-differentiabilitymentioning

confidence: 99%

“…In such a framework, some consequences of non-differentiability, both in the usual space (of the space and time coordinates) and in the scales space, are evident [10][11][12][15][16][17]: (i) any continuous but non-differentiable curve of the complex system's structural units (fractal curve) is explicitly dependent on scale resolution δω, i.e., its length tends to infinity when δω tends to zero; (ii) the physics of the complex system phenomena is related to the behavior of a functions set during the zoom operation of the scale δω. Then, through the substitution principle, δω will be identified with dω, i.e., δω = dω.…”

Section: Hallmarks Of Non-differentiabilitymentioning

confidence: 99%

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Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications

Grigorovici

Băcăiță

Pãun

et al. 2017

Entropy

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Abstract:In classical concepts, theoretical models are built assuming that the dynamics of the complex system's stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the "chameleon-like" behavior of cholesterol.

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Section: Pairs Generating Mechanisms: Implications In Dynamics Of Biomentioning

confidence: 99%

Section: Pairs Generating Mechanisms: Implications In Dynamics Of Biomentioning

confidence: 99%

Section: Hallmarks Of Non-differentiabilitymentioning

confidence: 99%

Section: Hallmarks Of Non-differentiabilitymentioning

confidence: 99%

See 2 more Smart Citations

Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications

Grigorovici

Băcăiță

Pãun

et al. 2017

Entropy

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“…In this way, not only the space, but the entire space-time continuum is considered to be non-differentiable and, therefore, fractal. In a such frame, we shall extend in the present paper the results from [12] by introducing the concept of relativistic non-differentiable entropy (non-differentiable entropy on a space-time manifold). Some of its characteristics and implications are also given.…”

Section: Introductionmentioning

confidence: 99%

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

Agop

Gavriluţ

Ştefan³

et al. 2015

Entropy

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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.).

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Brain Dynamics Explained by Means of Spectral-Structural Neuronal Networks

Agop

Gavriluţ

Crumpei

et al. 2020

12th Chaotic Modeling and Simulation International Conference

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Starting from the morphological-functional assumption of the fractal brain, a mathematical model is given by activating brain's non-differentiable dynamics through the determinism-nondeterminism inference of the responsible mechanisms. The postulation of a scale covariance principle in Schrödinger's type representation of the brain geodesics implies the spectral functionality of the brain dynamics through mechanisms of tunelling, percolation etc., while in the hydrodynamical type representation, it implies their structural functionality through mechanisms of wave schock, solitons type etc. For external constraints proportional with the states density, the fluctuations of the brain stationary dynamics activate both the spectral neuronal networks and the structural ones through a mapping principle of two distinct classes of cnoidal oscillation modes. The spectral-structural compatibility of the neuronal networks generates the communication codes of algebraic type, while the same compatibility on the solitonic component induces a strange topology (the direct product of the spectral topology and the structural one) that is responsible of the quadruple law (for instance, the nucleotide base from the human DNA structure). Implications in the elucidation of some neuropsychological mechanisms (memory's location and functioning, dementia etc.) are also presented.

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Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

Cited by 14 publications

References 35 publications

Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications

Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications

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

Brain Dynamics Explained by Means of Spectral-Structural Neuronal Networks

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