Some dynamical property of the Tsallis distribution from a Fokker－Planck equation

doi:10.1088/1674-1056/19/4/040501

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40501-040501.doi: 10.1088/1674-1056/19/4/040501

Some dynamical property of the Tsallis distribution from a Fokker－Planck equation

杜九林

Department of Physics, School of Science, Tianjin University, Tianjin 300072, China

收稿日期:2009-07-22 修回日期:2009-08-18 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.~10675088).

Some dynamical property of the Tsallis distribution from a Fokker－Planck equation

Du Jiu-Lin(杜九林)^†

Department of Physics, School of Science, Tianjin University, Tianjin 300072, China

Received:2009-07-22 Revised:2009-08-18 Online:2010-04-15 Published:2010-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.~10675088).

摘要/Abstract

摘要： This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.

Abstract: This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an arbitrary potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.

Key words: Tsallis distribution, dynamical property, Fokker--Planck equation

中图分类号: (Noise)

05.40.Ca

02.50.Ng (Distribution theory and Monte Carlo studies) 02.50.Ga (Markov processes)

杜九林. Some dynamical property of the Tsallis distribution from a Fokker－Planck equation[J]. 中国物理B, 2010, 19(4): 40501-040501.

Du Jiu-Lin(杜九林). Some dynamical property of the Tsallis distribution from a Fokker－Planck equation[J]. Chin. Phys. B, 2010, 19(4): 40501-040501.

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Some dynamical property of the Tsallis distribution from a Fokker－Planck equation

Some dynamical property of the Tsallis distribution from a Fokker－Planck equation

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