Effective-temperature concept: a physical application for nonextensive statistical mechanics

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2012-12, Vol.86 (6 Pt 1), p.061113-061113, Article 061113
• Main Authors: Nobre, Fernando D, Souza, Andre M C, Curado, Evaldo M F
• Format: Article
• Language: English
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.86.061113

The H-theorem [(df/dt) ≤ 0] for a free-energy functional, f = u-θs (with u and s representing, respectively, the internal energy and a generalized entropy of a given physical system), has been proven previously by making use of a nonlinear Fokker-Planck equation. Herein we focus on a nonlinear Fokker-Planck equation derived by means of a coarse-graining procedure on the equations of motion of a system of interacting vortices, under overdamped motion, in the absence of thermal noise (T = 0). In this case, we show that the parameter θ is directly related to the density as well as to the interactions among vortices. Generalized quantities such as entropy, internal energy, free energy, and heat capacity are analyzed for varying θ: important relations and physical behavior analogous to those of standard thermodynamics are found, showing that θ plays the role of an effective temperature. Estimates of θ in typical physical situations of different type-II superconductors are presented; in addition to this, possible experimental procedures for varying θ are proposed.