SciELO - Scientific Electronic Library Online

 
vol.62 número2First principles study of the effects of disorder in the Sr2FeMoO6 perovskiteCharacterization of thermal rectification in asymmetrical-structured materials with inhomogeneous mass distribution índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

  • No hay artículos similaresSimilares en SciELO

Compartir


Revista mexicana de física

versión impresa ISSN 0035-001X

Rev. mex. fis. vol.62 no.2 México mar./abr. 2016

 

Investigación

 

Entropy production: evolution criteria, robustness and fractal dimension

 

J.A. Betancourt-Mara, M. Rodríguez-Ricardb, R. Mansillac, G. Cochod,*, and J.M. Nieto-Villare,a

 

a Mexican Institute of Complex Systems, Tamaulipas, México,

b Departamento de Ecuaciones Diferenciales, Facultad de Matemática y Computación, Universidad de La Habana, La Habana 10400 Cuba.

c Centro de Investigaciones Interdisciplinarias en Ciencias y Humanidades, Universidad Nacional Autónoma de México.

d Departamento de Sistemas Complejos del Instituto de Física, Universidad Nacional Autónoma de México. * e-mail: cocho@fisica.unam.mx

e Department of Chemical-Physics, M.V. Lomonosov Chemistry Division, Faculty of Chemistry, & H. Poincare Group of Complex Systems, Physics Faculty, University of Havana, Havana 10400 Cuba.

 

Received 13 October 2015;
accepted 4 January 2016

 

Abstract

It was proved through Rossler model, where the funnel case is more robust tan spiral chaos, the entropy production per unit time is a Lyapunov's function on the space of the control system parameters. It was established the conjecture of entropy production fractal dimension. The current theoretical framework will hopefully provide a better understanding of the relationship between thermodynamics and nonlinear dynamics and contribute to unify theses through complex systems theory.

Keywords: Irreversible thermodynamics; complex systems; fractal dimension.

PACS: 05.45.Pq; 05.45.Df; 05.70.Ln

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

1. C. Beck and F. Schlogl, Thermodynamics of Chaotic Systems: An Introduction (Cambridge University Press, New York, 1993)        [ Links ]

2. Dimensions and Entropies in Chaotic Systems Quantification of Complex Behavior in Proceedings of an International Workshop at the Pecos River Ranch, New México 1985, edited by G. Mayer-Kress, (Springer-Verlag, Berlin, 1986).         [ Links ]

3. J.M. Nieto-Villar, R. Quintana and J. Rieumont, Physica Scripta 68 (2003) 163.         [ Links ]

4. J.M. Nieto-Villar, E. Izquierdo-Kulich, R. Quintana y J. Rieumont, Rev. Mex. Fis. 59(2013) 527        [ Links ]

5. W.G. Hoover and H.A. Posch, Phys. Rev. E 49 (1994) 1913.         [ Links ]

6. P. Gaspard, Adv. Chem. Phys. 135 83-133 2007.         [ Links ]

7. G. Nicolis, and I. Prigogine, Self-Organization in nonequilibrium systems (Wiley, New York, 1977).         [ Links ]

8. S.H. Strogatz, Nonlinear dynamics and chaos, (Westview Press, Boulder, 2000).         [ Links ]

9. O.E. Rossler, Phys. Lett. A 57 (1976) 397        [ Links ]

10. C.W. Gear in Proceedings of the IFIP Congress 68, Edinburgh, 1968 edited by A. J. H. Marvel, (New York: North-Holland, 1968) pp. 187-193.         [ Links ]

11. A. Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano, Physica D16 (1985)285.         [ Links ]

12. O.E. Rossler, Bull. Math. Biol. 39 (1977) 275.         [ Links ]

13. J.A. Betancourt-Mar and J.M. Nieto-Villar, Math. Biosci. Eng. 4 (2007) 177.         [ Links ]

14. A. Andronov, A. Vit, and C. Chaitin, Theory of Oscillators (Pergamon Press, Oxford, 1966).         [ Links ]

15. E. Izquierdo-Kulich, E. Alonso-Becerra and J.M. Nieto-Villar, J. Modern Physics 2 (2011) 615.         [ Links ]

16. J.D. Farmer, E. Ott, J.A. Yorke, Physica 7D (1983) 153.         [ Links ]

17. J.L. Kaplan, J.A. Yorke, Lect. Notes Math. 730 (1971) 204.         [ Links ]

18. G. Baier and S. Sahle, J. Chem. Phys. 100 (1994) 8907.         [ Links ]

19. J.M. Nieto-Villar, J. Betancourt-Mar, E. Izquierdo-Kulich, E. Tejera, Complejidad y Auto-organización en Patrones Naturales (editorial UH, 2013).         [ Links ]

20. H. Kitano, Molecular Systems biology 3 (2007) 137.         [ Links ]

21. J.A. Betancourt-Mar, V.A. Mendez-Guerrero, C. Hernández Rodríguez and J.M. Nieto-Villar, Math. Biosci. Eng. 13 (2010) 553.         [ Links ]

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons