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Journal
2013 | 11 | 7 | 910-914
Article title

Fluctuation of gauge field for general nonlinear Fokker-Planck equation and covariant version of Fisher information matrix

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Languages of publication
EN
Abstracts
EN
We clarify a strong link between general nonlinear Fokker-Planck equations with gauge fields associated with nonequilibrium dynamics and the Fisher information of the system. The notion of Abelian gauge theory for the non-equilibrium Fokker-Planck equation has proposed in the literature, in which the associated curvature represents internal geometry. We present the fluctuation of the gauge field can be decomposed into three parts. We further show that if we define the Fisher information matrix by using a covariant derivative then it gives correlation of the flux components but it is not gauge invariant.
Publisher

Journal
Year
Volume
11
Issue
7
Pages
910-914
Physical description
Dates
published
1 - 7 - 2013
online
17 - 10 - 2013
Contributors
author
  • Department of Mathematics and Physics, Faculty of Science, Kanagawa University, 2946, 6-233 Tsuchiya, Hiratsuka, Kanagawa, 259-1293, Japan, yamano@amy.hi-ho.ne.jp
References
  • [1] T. D. Frank, Nonlinear Fokker-Planck Equations: Fundamentals and Applications (Springer, Berlin, 2005)
  • [2] H. Feng, J. Wang, J. Chem. Phys. 135, 234511 (2011) http://dx.doi.org/10.1063/1.3669448[Crossref]
  • [3] M. E. Peskin, D. V. Schroeder, An Introduction to Quantum Field Theory (Perseus Books Publishing, Cambridge Massachusetts, 1995) Ch.15.
  • [4] T. Cover, J. Thomas, Elements of Information Theory 2nd ed. (Wiley-Interscience, New Jersey, 2006)
  • [5] B. R. Frieden, Science from Fisher Information - A Unification (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO9780511616907[Crossref]
  • [6] D. Brody, B. Meister, Phys. Lett. A 204, 93 (1995) http://dx.doi.org/10.1016/0375-9601(95)00487-N[Crossref]
  • [7] T. Yamano, J. Math. Phys. 53, 043301 (2012) http://dx.doi.org/10.1063/1.3700757[Crossref]
  • [8] G. A. Casas, F. D. Nobre, E. M. F. Curado, Phys. Rev. E 86, 061136 (2012) http://dx.doi.org/10.1103/PhysRevE.86.061136[Crossref]
  • [9] H. Fujisaka, Statistical mechanics of nonequilibrium systems (Sangyo-tosho, Tokyo, 1998) (in Japanese)
  • [10] T. Yamano, Eur. Phys. J. B 86, 363 (2013) http://dx.doi.org/10.1140/epjb/e2013-40634-9[Crossref]
  • [11] G. E. Crooks, Fisher Information and Statistical Mechanics, Tech. Note 008v4 (2012), http://threeplusone.com/Crooks-FisherInfo.pdf
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0290-5
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