Nobre Fernando D, Souza Andre M C, Curado Evaldo M F
Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):061113. doi: 10.1103/PhysRevE.86.061113. Epub 2012 Dec 10.
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.
自由能泛函(f = u - \theta s)（其中(u)和(s)分别表示给定物理系统的内能和广义熵）的(H)定理([(df/dt) \leq 0])，此前已通过使用非线性福克 - 普朗克方程得到证明。在此，我们关注在无热噪声（(T = 0)）的过阻尼运动情况下，通过对相互作用涡旋系统的运动方程进行粗粒化过程导出的非线性福克 - 普朗克方程。在这种情况下，我们表明参数(\theta)与涡旋的密度以及涡旋之间的相互作用直接相关。针对不同的(\theta)分析了诸如熵、内能、自由能和热容量等广义量：发现了与标准热力学类似的重要关系和物理行为，表明(\theta)起到有效温度的作用。给出了不同II型超导体典型物理情形下(\theta)的估计值；除此之外还提出了改变(\theta)的可能实验方法。
