Maximum Path Information and Fokker--Planck Equation
LI Wei1,2, Q. A. Wang2, A. Le Mehaute2
1Complexity Science Center and Institute of Particle Physics, Huazhong Normal University, Wuhan 4300792Institut Superieur des Materiaux du Mans, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France
Maximum Path Information and Fokker--Planck Equation
LI Wei1,2;Q. A. Wang2;A. Le Mehaute2
1Complexity Science Center and Institute of Particle Physics, Huazhong Normal University, Wuhan 4300792Institut Superieur des Materiaux du Mans, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France
摘要We present a rigorous method to derive the nonlinear Fokker--Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons & Fractals 23(2005)1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy [J. Stat. Phys. 52(1988)479] and the time t.
Abstract：We present a rigorous method to derive the nonlinear Fokker--Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons & Fractals 23(2005)1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy [J. Stat. Phys. 52(1988)479] and the time t.
LI Wei;Q. A. Wang;A. Le Mehaute. Maximum Path Information and Fokker--Planck Equation[J]. 中国物理快报, 2008, 25(4): 1165-1167.
LI Wei, Q. A. Wang, A. Le Mehaute. Maximum Path Information and Fokker--Planck Equation. Chin. Phys. Lett., 2008, 25(4): 1165-1167.
[1] Wang Q A 2005 Chaos, Solitons & Fractals 23 1253 [2] Tsallis C 1988 J. Stat. Phys. 52 479 [3] Fokker A D 1914 Ann. Physik 43 810 [4] Planck M 1917 Sitzber. Preuss. Akad. Wiss. p324 [5] Uhlenbeck G E and Ornstein L S 1930 Phys. Rev. 36 832 [6] Chandrasekhar S 1943 Rev. Mod. Phys. 15 1 [7] Wang M C and Uhlenbeck G E 1945 Rev. Mod. Phys. 17 323 [8] Haken H 1975 Rev. Mod. Phys. 47 67 [9] Schuss Z 1980 Theory and Applications of StochasticDifferential Equations (New York: Wiley) [10] Risken H 1984 The Fokker--Planck Equation (Berlin: Springer) [11] Shannon C E 1948 Bell System Tech. J. 27 379 Shannon C E 1948 Bell System Tech. J. 27 623 [12] Tsallis C 1994 New Trends in Magnetism, MagneticMaterials and Their Applications (New York: Plenum) p 451 [13] Prato D 1995 Phys. Lett. A 203 165 [14] Wang Q A, Bangoupa S, Dzanguea F, Jeatsaa A, Tsobnanga F and LeM\'ehaut\'e A 2008 Chaos, Solitons $\&$ Fractals (in press) [15] Michael F and Johnson M D 2003 Physica A 324359 [16] Tsallis C and Bukman D J 1996 Phys. Rev. E 54 2197 [17] Wang Q A 2004 Chaos, Solitons $\&$ Fractals 19 639 [18] Wang Q A, Le M\'ehaut\'e A, Nivanen L and Pezeril M 2004 Physica A 340 117
2008, Vol. 25 
