Non-distributive algebraic structures derived from nonextensive statistical mechanics
نویسندگان
چکیده
We propose a two-parametric non-distributive algebraic structure that follows from (q, q)-logarithm and (q, q)-exponential functions. Properties of generalized (q, q)operators are analyzed. We also generalize the proposal into a multi-parametric structure (generalization of logarithm and exponential functions and the corresponding algebraic operators). All n-parameter expressions recover (n− 1)-generalization when the corresponding qn → 1. Nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures, in which this work is a consequence.
منابع مشابه
Generalized symmetric nonextensive thermostatistics and q-modified structures
We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q ↔ q−1 symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of non-symmetric Tsallis statistics. Basic properties and analogies with quantum groups are discussed. PACS: 05.20.-y; 0...
متن کاملNonextensive statistical mechanics for rotating quasi-two-dimensional turbulence
We have conducted experiments on an asymmetrically forced quasi-two-dimensional turbulent flow in a rapidly rotating annulus. Assuming conservation of potential enstrophy and energy, we maximize a nonextensive entropy function to obtain the azimuthally averaged vorticity as a function of radial position. The predicted vorticity profile is in good accord with the observations. A nonextensive for...
متن کاملGeneralized statistical mechanics and fully developed turbulence
The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating fr...
متن کاملNonextensive statistical mechanics for hybrid learning of neural networks
This paper introduces a new hybrid approach for learning systems that builds on the theory of nonextensive statistical mechanics. The proposed learning scheme uses only the sign of the gradient, and combines adaptive stepsize local searches with global search steps that make use of an annealing schedule inspired from nonextensive statistics, as proposed by Tsallis. The performance of the hybrid...
متن کاملProbabilistic properties of nonextensive thermodynamic
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a qdeformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the Tsallis entropy depends on the deformation parameter and must be redefined to recover the usual thermodynamic relations. The notions of variance and covarianc...
متن کامل