A variational perturbation approximation method in Tsallis non-extensive statistical physics

作者：Lu, Wen Fa^*; Cai, Tuo; Kim, Chul Koo

来源：Physica A: Statistical Mechanics and Its Applications , 2007, 378(2): 255-272.

DOI：10.1016/j.physa.2006.11.087

• non-extensive effect
• Tsallis entropy
• variational perturbation theory

For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order in variational perturbation expansion. The approximation up to the first order amounts to a variational approach which covers the variational method developed by E.K. Lenzi, L.C. Malacarne, R.S. Mendes [Phys. Rev. Lett. 80 (1998) 218] and the approximations up to higher orders can systematically improve variational results. As an illustrated example, the generalized free energy for a classical harmonic oscillator (considered in the Lenzi's joint work) are calculated up to the third order, and the resultant approximations up to the first, second, and third orders are numerically compared with the exact result.

• 出版日期2007-5-15
• 单位黔南民族师范学院; 上海交通大学