Fractal Information by Means of Harmonic Mappings and Some Physical Implications

Entropy

卷:18

Viorel Puiu Păun¹  Maricel Agop²  Florin Alexandru Luca³  Dumitru Filipeanu³  Liliana Topliceanu⁴  Alina Gavriluţ⁵  Constantin Grecea⁶ 

[1] Department of Physics, Faculty of Applied Sciences, Politehnica University of Bucharest, Bucharest 060042, Romania;

[2] Department of Physics, Gheorghe Asachi Technical University of Iaşi, Iaşi 700506, Romania;

[3] Economic and Marketing Department, Technical University Gheorghe Asachi from Iaşi, Iaşi 700050, Romania;

[4] Faculty of Engineering, University ”Vasile Alecsandri” of Bacău, Bacău 600115, Romania;

[5] Faculty of Mathematics, Alexandru Ioan Cuza (Al.I. Cuza) University, Iaşi 700506, Romania;

[6] Faculty of Physics, Alexandru Ioan Cuza (Al.I. Cuza) University, Iaşi 700506, Romania;

关键词: fractal information;    fractal entropy;    variational principle;    mapping;    economy;    econometrics;    management;    economic statistics;   

DOI  :  10.3390/e18050160

来源: DOAJ

【 摘 要 】

Considering that the motions of the complex system structural units take place on continuous, but non-differentiable curves, in the frame of the extended scale relativity model (in its Schrödinger-type variant), it is proven that the imaginary part of a scalar potential of velocities can be correlated with the fractal information and, implicitly, with a tensor of “tensions”, which is fundamental in the construction of the constitutive laws of material. In this way, a specific differential geometry based on a Poincaré-type metric of the Lobachevsky plane (which is invariant to the homographic group of transformations) and also a specific variational principle (whose field equations represent an harmonic map from the usual space into the Lobachevsky plane) are generated. Moreover, fractal information (which is made explicit at any scale resolution) is produced, so that the field variables define a gravitational field. This latter situation is specific to a variational principle in the sense of Matzner–Misner and to certain Ernst-type field equations, the fractal information being contained in the material structure and, thus, in its own space associated with it.

【 授权许可】

Unknown