Implications of Non-Differentiable Entropy on a Space-Time Manifold
AbstractAssuming 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.). View Full-Text
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Agop, M.; Gavriluţ, A.; Ştefan, G.; Doroftei, B. Implications of Non-Differentiable Entropy on a Space-Time Manifold. Entropy 2015, 17, 2184-2197.
Agop M, Gavriluţ A, Ştefan G, Doroftei B. Implications of Non-Differentiable Entropy on a Space-Time Manifold. Entropy. 2015; 17(4):2184-2197.Chicago/Turabian Style
Agop, Maricel; Gavriluţ, Alina; Ştefan, Gavril; Doroftei, Bogdan. 2015. "Implications of Non-Differentiable Entropy on a Space-Time Manifold." Entropy 17, no. 4: 2184-2197.