Over the non-extensivity parameter for some superadditives systems

Authors

  • R. Borja–Tamayo Universidad EAFIT
  • C. Cartagena Marín Universidad EAFIT
  • Gabriel Ignacio Loaiza Ossa Universidad EAFIT
  • G. Molina Vélez Universidad EAFIT
  • María Eugenia Puerta Yepes Universidad EAFIT

Keywords:

entropy, thermostatistics non expansive, super–additives systems

Abstract

In this paper one introduces a bijective relation between the non–extensivity parameter q and the stationary probability density function f corresponding to an observable u for some super–additive systems for which the notion of Tsallis entropy applies. This relation is given as a comparison of linking functions characterizing memoryless of certain random variables associated to parameter q and the stationary density f. Then these results are used to formulate a method for approximating the parameter q based on an estimation of f, provided that the effective energy associated to u equals the effective kinetic energy.

PACS: 05.20.Jj , 05.70.Ce

MSC: 46N55, 28D20

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Author Biographies

  • R. Borja–Tamayo, Universidad EAFIT

    Magíster en Matemáticas aplicadas, profesor

  • C. Cartagena Marín, Universidad EAFIT

    Físico, profesor,

  • Gabriel Ignacio Loaiza Ossa, Universidad EAFIT

    Doctor en Matemáticas, profesor,

  • G. Molina Vélez, Universidad EAFIT

    Magíster en Matemáticas aplicadas, profesor

  • María Eugenia Puerta Yepes, Universidad EAFIT

    Doctora en Matemáticas, profesora,

References

C. Tsallis. Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical Physics, ISSN 0022–4715, 52(1 y 2), 478–487 (1988).

C. Tsallis. Nonextensive entropy: Interdisciplinary applications, ISBN 0195159772, Gell–Mann, M.(Editores), 2004.

M. Ghitany. Some remarks on a characterization of the generalized log-logistic distribution. Environmetrics, ISSN 1180–4009, 7(3), 277–281 (1996).

C. Tsallis, F. Baldovin, R. Cerbino and P. Pierobon. Entropic nonextensivity: a possible measure of complexity. Chaos, Solitons and Fractals, ISSN 0960–0779, 13(3), 371–391 (2002).

C. Beck. Application of generalized thermostatistics to fully developed turbulence. Physica A: Statistical Mechanics and its Applications, ISSN 0378–4371, 277(1), 115–123 (2000).

C. Tsallis, R. Mendes and A. Plastino. The role of constraints within generalized nonextensive statistics. Physica A: Statistical Mechanics and its Applications, ISSN 0378–4371, 261(3), 534–554 (1998).

G. Ferri, S. Martínez y A. Plastino. Sobre el procedimiento de normalización en la termoestadística de Tsallis. Anales AFA, ISSN 0327–358X, 16, 24–29 (2004).

L. Moyano. Mecˆanica estatística n˜ao-extensiva em sistemas complexos: fundamentos dinˆamicos e aplica¸c˜oes, Tese de Dutorado, Centro Brasilero de Pesquisas Físicas, Rio de Janeiro (2006), http://cbpfindex.cbpf.br/publication_ pdfs/tese_moyano.2006_05_02_04_01_11.pdf.

J. Naudts. Deformed exponentials and logarithms in generalized thermostatistics. Physica A: Statistical Mechanics and its Applications, ISSN 0378–4371, 316(1), 323–334 (2002).

E. Pinheiro Borges. Manifesta¸c˜oes dinˆamicas e termodinˆamicas de sistemas n˜ao- extensivos, Tese de Dutorado, Centro Brasileiro de Pesquisas Físicas. Rio de Janeiro (2004), http://www2.ufba.br/ ernesto/files/epb-tese.pdf.

E. Daniels, C. Beck and E. Bodenschatz. Defect turbulence and generalized statistical mechanics. Physica D: Nonlinear Phenomena, ISSN 0167–2789, 193(1–4), 208–217 (2004).

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How to Cite

Borja–Tamayo, R., Cartagena Marín, C., Loaiza Ossa, G. I., Molina Vélez, G., & Puerta Yepes, M. E. (2010). Over the non-extensivity parameter for some superadditives systems. Ingeniería Y Ciencia, 6(11), 143-158. https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/254

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