Implications of Quantum Informational Entropy in Some Fundamental Physical and Biophysical Models

Abstract

Correspondingly, the theoretical models that describe the complex systems dynamics become more and more advanced [ -]. For all that, this problem can be solved by taking into account that the complexity of the interaction process implies various temporal resolution scales, and the pattern evolution implies different degrees of freedom [ ].[In order to develop new theoretical models we must state the fact that the complex systems displaying chaotic behavior are recognized to acquire self-similarity space-time structures can appear in association with strong fluctuations at all possible space-time scales [ -]. "fterwards, for temporal scales that are large with respect to the inverse of the highest Lyapunov exponent, the deterministic trajectories are replaced by a set of potential trajectories and the concept of definite positions by that of probability density] [ ]. "n interesting example is the collisions processes in complex systems, where the dynamics of the particles can be described by non-differentiable curves.Since non-differentiability can be considered a universal property of complex systems, it is mandatory to develop a non-differentiable physics. In this way, by considering that the complexity of the interaction processes is replaced by non-differentiability, using the entire range of quantities from the standard physics differentiable physics is no longer required [ ].This topic was developed in the Scale Relativity Theory SRT [ , ] and in the non-standard Scale Relativity Theory NSSRT [ -]. [In the framework of SRT or NSSRT we assume that the movements of complex system entities take place on continuous but non-differentiable curves fractal curves so that all physical phenomena involved in the dynamics depend not only on the space-time coordinates but also on the space-time scales resolution. In this conjecture, the physical quantities that describe the dynamics of complex systems can be considered as fractal functions. In addition, the entities of the complex system may be reduced to and identified with their own trajectories. In this way, the complex system's behavior will be identical to the one of a special interaction-less fluid by means of its geodesics in a nondifferentiable fractal space] [ , , ].In such context notions as informational entropy, Onicescu informational energy etc become important in the Nature description. These notions will be correlated with the fractal part of the physical quantities that describe the dynamics of complex systems. . Informational entropy and energyIndependently of scale resolution, the motion, either on infragalactic scale for instance, the planetary motion , or on atomic scale for instance, the motion of the electron around its nucleus takes place on conics ellipses . Such motion in invariant with respect to the SL R group. In what follows, we shall consider this invariance only with respect to the motion on atomic scale. . . SL R invariance and canonic formalismSL R group is the group of transformations [ -]

Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion

“…In this case, solely nocturnal profiles have been chosen from the beginning of the time series. As can be seen in the temperature profile figures, the theoretical model predicts the inversion at the boundary layer, although once again, it does not always accurately predict the altitude at which the inversion takes place (Figures [19][20][21][22]. This is because the model has not been adjusted to account for any surface radiative effects, merely taking into consideration the effects of the boundary layer.…”

“…Through Equations ( 12) and ( 13) and using the mathematical procedures from [21][22][23], Equation (8) reduces to the multifractal hydrodynamic equations:…”