Variational approach and deformed derivatives

J. Weberszpil and J.A. Helayël-Neto

Physica A: Statistical Mechanics and its Applications, 2016, vol. 450, issue C, 217-227

Abstract: Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis’ framework and the Kaniadakis’ scenario, with a local form of fractional-derivative operators for fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. Here, in this paper, we present an extension of the traditional calculus of variations for systems containing deformed-derivatives embedded into the Lagrangian and the Lagrangian densities for classical and field systems. The results extend the classical Euler–Lagrange equations and the Hamiltonian formalism. The resulting dynamical equations seem to be compatible with those found in the literature, specially with mass-dependent and with nonlinear equations for systems in classical and quantum mechanics. Examples are presented to illustrate applications of the formulation. Also, the conserved ​Noether current is worked out.

Keywords: Deformed derivatives; Metric derivatives; Fractal continuum; Generalized statistical mechanics; Variational principle; Position-dependent mass (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:450:y:2016:i:c:p:217-227

DOI: 10.1016/j.physa.2015.12.145

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