Lambert function and a new non-extensive form of entropy

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 72, Issue 6, 2007, Pages 785-800

  Shafee, Fariel ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Free energy; Lambert function; Non extensive entropy; Probability distribution function

Indexed keywords

ENTROPY; OPTIMIZATION; PARAMETERIZATION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; SPECIFIC HEAT;

LAMBERT FUNCTION; TRANSCENDENTAL EQUATION; TSALLIS ENTROPY;

THERMODYNAMICS;

EID: 36549009192     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxm039     Document Type: Article

References (28)

1. ACZEL, J. & DAROCZY, Z. (1963a) Charakterisierung der Entropien positiver Ordnung und der Shannonschen Entropie. Acta Math. Acad. Sci. Hung., 14, 95-121.
2. ACZEL, J. & DAROCZY, Z. (1963b) Sur la caractrisation axiomatique des entropies d'ordre positif, y comprise l'entropie de Shannon. C. R. Acad. Sci. (Paris), 257, 1581-1584.
3. ANTENEODO, C. & TSALLIS, C. (1997) Two-dimensional turbulence in pure-electron plasma: A nonextensive thermostatistical description. J. Mol. Liq., 71, 255-267.
4. BECK, C. (2000) Nonextensive statistical mechanics and particle spectra. Physica A, 286, 164-180.
5. BOGHOSIAN, B. M. (1995) Thermodynamic description of two-dimensional Euler turbulence using Tsallis statistics. Phys. Rev. E, 53, 4754-4763.
6. BORLAND, L. (1998) Microscopic dynamics of the nonlinear Fokker-Planck equation: A phenomenological model. Phys. Rev. E, 57, 6634-6642.
7. BUIATTI, M., GRIGOLINI, P. & MONTAGNINI, A. (1999) Dynamic approach to the thermodynamics of superdiffusion. Phys. Rev. Lett. 82, 3383-3387.
8. CORLESS, R. M., GONNET, G. H., HARE, D. E. G., JEFFREY, D. J. & KNUTH, D. E. (1996) On the Lambert W function. Adv. Comput. Math. 5, 329-359.
9. ESTEBAN, M. D. & MORALES, D. (1995) A summary on entropy statistics. Kybernetika, 31, 337-346.
10. GRIGOLINI, P., TSALLIS, C. & WEST, B. J. (2001) Classical and quantum complexity and nonextensive thermodynamics. Chaos Fractals Solitons, 13, 367-370.
11. HAMITY, V. H. & BARRACO, D. E. (1996) Generalized nonextensive thermodynamics applied to the cosmic background radiation in a Robertson-Walker universe. Phys. Rev. Lett., 76, 4664-4666.
12. KANIADAKIS, G. (2001) Nonlinear kinetics underlying generalized statistics. Physica A, 296, 405.
13. KANIADAKIS, G. (2002) Statistical mechanics in the context of special relativity. Phys. Rev. E, 66, 056125.
14. KINCHIN, A. I. (1957) Mathematical Foundations of Information Theory. New York: Dover Publications.
15. LANDSBERG, P. T. (1999) Entropies galore. Braz. J. Phys., 29, 46-49.
16. LYRA, M. L. & TSALLIS, C. (1998) Nonextensivity and multifractality in low-dimensional dissipative systems. Phys. Rev. Lett., 80, 53-56.
17. NIELSEN, M. A. & CHUANG, M. (2000) Quantum Computation and Quantum Information. New York: Cambridge University Press.
18. PATHRIA, R. K. (1996) Statistical Mechanics. Oxford, UK: Butterworth-Heinemann, p. 77.
19. PLASTINO, A. R. & PLASTINO, A. (1994) The classical N-body problem within a generalized statistical mechanics. J. Phys. A, 27, 5707-5714.
20. PLASTINO, A. R. & PLASTINO, A. (1995) Non-extensive statistical mechanics and generalized Fokker-Planck equation. Physica A, 222, 347-354.
21. RENYI, A. (1970) Probability Theory. Amsterdam: North-Holland.
22. SOTOLONGO-COSTA, O., GUZMAN, F. & RODGERS, G. J. (2004) Fingerprints of non-extensivity in DNA fragment distributions. Revista cubana de Fisica, 21, 29-32.
23. TSALLIS, C. (1988) Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 52, 479-487.
24. TSALLIS, C. & BUKMAN, D. J. (1996) Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis. Phys. Rev. E, 54, R2197-R2200.
25. TSALLIS, C., PLASTINO, A. R. & ZHENG, W.-M. (1997) Power-law sensitivityto initial conditions: New entropic representation. Chaos Solitons Fractals, 8, 885-891.
26. WANG, Q. A. (2003) Extensive generalization of statistical mechanics based on incomplete information theory. Entropy, 5 220-232.
27. WOLF, C. (2002) Equation of state for photons admitting Tsallis statistics. Fizika B, 11, 1.
28. VALLURI, S. R., CORLESS, R. M. & JEFFREY, D. J. (2000) Some applications of the Lambert W function to physics. Can. J. Phys., 78, 823-831.