Unique additive information measures-Boltzmann-Gibbs-Shannon, Fisher and beyond

Physica A: Statistical Mechanics and its Applications

Volumn 365, Issue 1, 2006, Pages 28-33

  Van P ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Additivity; Fisher information; Non extensive statistics; Schr dinger Madelung equation

Indexed keywords

NONLINEAR EQUATIONS; PROBABILITY DISTRIBUTIONS;

ADDITIVITY; FISHER INFORMATION; NON-EXTENSIVE STATISTICS; SCHRÖDINGER-MADELUNG EQUATION;

INFORMATION THEORY;

EID: 33645972263     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.01.027     Document Type: Article

References (21)

1. Jaynes E.T. Information theory and statistical mechanics. Phys. Rev. 106 4 (1957) 620-630
2. Rényi A. On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematics and Statistical Probability, 1960 vol. I (1961), University of California Press, Berkeley 547-561
3. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52 (1988) 479-487
4. Kaniadakis G. Non-linear kinetics underliying generalized statistics. Physica A 296 (2001) 405-425
5. Cohen E.G.D. Statistics and dynamics. Physica A 305 (2002) 19-26
6. Beck C., and Cohen E.G.D. Superstatistics. Physica A 321 (2003) (cond-mat/0205097)
7. Fisher R.A. Statistical Methods and Scientific Inference (1959), Oliver and Boyd, Edinburgh-London
8. Borovkov A.A. Mathematical Statistics (1998), Gordon and Breach Science Publishers, London
9. Frieden B.R. Physics from Fisher Information (a Unification) (1998), Cambridge University Press, Cambridge
10. Plastino A., Plastino A.R., and Casas M. Fisher variational principle and thermodynamics. In: Sieniutycz S., and Farkas H. (Eds). Variational and Extremum Principles in Macroscopic Problems (2005), Elsevier, Amsterdam 379-394
11. Mackey M.C. Time's Arrow: The Origins of Thermodynamic Behaviour (1992), Springer, New York
12. Kaniadakis G., Lissia M., and Scarfone A.M. Deformed logarithms and entropies. Physica A 340 (2004) 41-49
13. Frieden B.R., Plastino A., Plastino A.R., and Soffer B.H. Scrödinger link between nonequilibrium themrodynamics and Fischer information. Phys. Rev. E 66 (2002) 046128
14. Reginatto M. Derivation of the equation of nonrelativistic quantum mechanics using the principle of minimum Fischer information. Phys. Rev. A 58 3 (1998) 1775-1778
15. Hall M.J.W., and Reginatto M. Shchrödinger equation from an exact uncertainty principle. J. Phys. A 35 (2002) 3289-3303 (quant-ph/0102069)
16. Hall M.J.W., and Reginatto M. Quantum mechanics form a Heisenberg-type equality. Fortschr. Phys. 50 (2002) 646-651 (quant-ph/0201084)
17. P. Ván, T. Fülöp, Weakly nonlocal fluid mechanics-the Schrödinger equation, 2003 (quant-ph/0304062).
18. Bialynicki-Birula I., and Mycielski J. Nonlinear wave mechanics. Ann. Phys. 100 (1976) 62-93
19. Wang C.C. A new representation theorem for isotropic functions: an answer to professor G. F. Smith's criticism of my papers on representations of isotropic functions, Part 1, Scalar valued isotropic functions. Arch. Rat. Mech. Anal. 36 3 (1970) 166-197
20. Plastino A.R., and Plastino A. Non-extensive statistical mechanics and generalized Fokker-Planck equation. Physica A 222 (1995) 347-354
21. Frieden B.R. Fischer information, disorder, and the equilibrium distributions of physics. Phys. Rev. A 41 8 (1990) 4265-4276