科研之友
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摘要
The theory and application of nonextensive statistical mechanics (NESM) have underwent rapid development since the nonextensive entropy is put forward in 1988; its tentacles are almost throughout all areas of physics and has been a huge success. The nonextensive distribution function, however, as a basic part of NESM theory and application foundation, suffers a controversy: two different mathematical definitions of nonextensive distributions. Here, we show that the one dimensional nonextensive distribution function has the form of [1 + (1 - q)x(2)](1/q-1). We are starting from the nonextensive entropy, derive the nonextensive distribution function adopting the Maxwellian method, and prove the correctness of the form, and illustrate the physical meaning of the nonextensive parameter q as the fractal dimension when the Euclidean dimension is one. Furthermore, we derive the three-dimensional distribution function and the relativistic nonextensive distribution function, which perfect the theory of NESM and lay a solid application foundation of the NESM. We use the relativistic nonextensive distribution function to investigate the dispersion relations of relativistic longitudinal oscillation in nonextensive plasma and obtain the analytical expression of long wave dispersion relations under the ultra-relativistic case and the complete numerical dispersion curves. These results under an extensive limit reproduce Maxwellian statistical results. The proposed theory provides a method to measure the dimension of a plasma system, which may greatly promote our understanding for complex nonlinear plasma systems and thus, promote the understanding and solving of nonlinear problems such as turbulence, chaos, and soliton. This work also is the application foundation of nonextensive statistical mechanics to high energy physics such as relativistic plasma, M-theory, and so on in physical and mathematical aspects. Published by AIP Publishing.
- 出版日期2018-10
- 单位南昌大学
