2013/10/31 by Masamichi Ishihara
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Dust and Plasma Wave Phenomena #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1142/s0217979214502348
published as Int. J. Mod. Phys. B, 29, 1450234 (2015) · Abstract was rewritten
arxiv created 2013/11/01 · openalex publication_date 2014/10/03 · arxiv updated 2014/12/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study the effects of the environment described by the Tsallis nonextensive statistics on physical quantities using an optimization method in the case of small deviation from the Boltzmann–Gibbs statistics. The x 4 model is used and the density operator is restricted to be a Gaussian form. The variational parameter is the frequency Ω of a harmonic oscillator in the optimization method. We obtain an approximate expression of free energy and of the expectation value of βmΩ 2 x 2 /2, where β is the inverse of the temperature T and m is the mass. The optimized frequency is estimated numerically. The expectation value of βmΩ 2 x 2 /2 and the derivative of the energy with respect to the temperature [Formula: see text] are also calculated numerically. The effects of the Tsallis nonextensive statistic in the case of small deviation from the Boltzmann–Gibbs statistics are found: (1) the frequency modulation, (2) the variation of the expectation value of βm Ω 2 x 2 /2 and (3) the variation of [Formula: see text].