Dynamical scenario for nonextensive statistical mechanics

Physica A: Statistical Mechanics and its Applications

Volumn 340, Issue 1-3, 2004, Pages 1-10

  Tsallis, Constantino ^a,b  

^a CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

^b SANTA FE INSTITUTE   (United States)

Author keywords

Metastable states; Mixing; Nonextensive statistical mechanics; Nonlinear dynamics; Weak chaos

Indexed keywords

CHAOS THEORY; COMPUTATIONAL METHODS; ENTROPY; HAMILTONIANS; LYAPUNOV METHODS; MATHEMATICAL MODELS; THERMODYNAMICS;

METASTABLE STATES; MICROSCOPIC DYNAMICS; NONEXTENSIVE STATISTICAL MECHANICS; WEAK CHAOS;

STATISTICAL MECHANICS;

EID: 3042789122     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2004.03.072     Document Type: Conference Paper

References (37)

1. Einstein A. Annalen der Physik. 33:1910;1275. ["Usually W is put equal to the number of complexions... In order to calculate W , one needs a complete (molecular-mechanical) theory of the system under consideration. Therefore it is dubious whether the Boltzmann principle has any meaning without a complete molecular-mechanical theory or some other theory which describes the elementary processes. S=(R/N)log W+ const. seems without content, from a phenomenological point of view, without giving in addition such an Elementartheorie."] (Translation: Abraham Pais, Subtle is the Lord... Oxford University Press, 1982)].
2. Einstein A. Annalen der Physik. 33:1910;1275. ["Usually W is put equal to the number of complexions... In order to calculate W , one needs a complete (molecular-mechanical) theory of the system under consideration. Therefore it is dubious whether the Boltzmann principle has any meaning without a complete molecular-mechanical theory or some other theory which describes the elementary processes. S=(R/N)log W+ const. seems without content, from a phenomenological point of view, without giving in addition such an Elementartheorie."] (Translation: Abraham Pais, Subtle is the Lord ... Oxford University Press, 1982)].
3. Cohen E.G.D. Physica A. 305:2002;19 Baranger M. Physica A. 305:2002;27.
4. Cohen E.G.D. Physica A. 305:2002;19 Baranger M. Physica A. 305:2002;27.
5. Tsallis C. J. Stat. Phys. 52:1988;479 Curado E.M.F., Tsallis C. J. Phys. A. 24:1991;L69. [Corrigenda: 24 (1991) 3187 (1991) and 25 (1992) 1019] Tsallis C., Mendes R.S., Plastino A.R. Physica A. 261:1998;534. ; For a recent review see M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy - Interdisciplinary Applications; Oxford University Press, New York, 2004; For full bibliography see http://tsallis.cat.cbpf.br/biblio.htm.
6. Tsallis C. J. Stat. Phys. 52:1988;479 Curado E.M.F., Tsallis C. J. Phys. A. 24:1991;L69. [Corrigenda: 24 (1991) 3187 (1991) and 25 (1992) 1019] Tsallis C., Mendes R.S., Plastino A.R. Physica A. 261:1998;534. ; For a recent review see M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy - Interdisciplinary Applications; Oxford University Press, New York, 2004; For full bibliography see http://tsallis.cat.cbpf.br/biblio.htm.
7. Tsallis C. J. Stat. Phys. 52:1988;479 Curado E.M.F., Tsallis C. J. Phys. A. 24:1991;L69. [Corrigenda: 24 (1991) 3187 (1991) and 25 (1992) 1019] Tsallis C., Mendes R.S., Plastino A.R. Physica A. 261:1998;534. ; For a recent review see M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy - Interdisciplinary Applications; Oxford University Press, New York, 2004; For full bibliography see http://tsallis.cat.cbpf.br/biblio.htm.
8. Tsallis C. J. Stat. Phys. 52:1988;479 Curado E.M.F., Tsallis C. J. Phys. A. 24:1991;L69. [Corrigenda: 24 (1991) 3187 (1991) and 25 (1992) 1019] Tsallis C., Mendes R.S., Plastino A.R. Physica A. 261:1998;534. ; For a recent review see M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy - Interdisciplinary Applications; Oxford University Press, New York, 2004; For full bibliography see http://tsallis.cat.cbpf.br/biblio.htm.
9. Tsallis C. J. Stat. Phys. 52:1988;479 Curado E.M.F., Tsallis C. J. Phys. A. 24:1991;L69. [Corrigenda: 24 (1991) 3187 (1991) and 25 (1992) 1019] Tsallis C., Mendes R.S., Plastino A.R. Physica A. 261:1998;534. ; For a recent review see M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy - Interdisciplinary Applications; Oxford University Press, New York, 2004; For full bibliography see http://tsallis.cat.cbpf.br/biblio.htm.
10. Tsallis C. Quimica Nova. 17:1994;468 see also C. Tsallis, in: S. Abe, Y. Okamoto (Eds.), Nonextensive Statistical Mechanics and its Applications, Series Lecture Notes in Physics, Springer, Heidelberg, 2001, 3p. (Appendix).
11. Tsallis C. Quimica Nova. 17:1994;468 see also C. Tsallis, in: S. Abe, Y. Okamoto (Eds.), Nonextensive Statistical Mechanics and its Applications, Series Lecture Notes in Physics, Springer, Heidelberg, 2001, 3p. (Appendix).
12. Tsallis C., Plastino A.R., Zheng W.-M. Chaos, Solitons and Fractals. 8:1997;885.
13. Baldovin F., Robledo A. Phys. Rev. E. 66:2002;045104(R) F. Baldovin, A. Robledo, cond-mat/0304410 Phys. Rev. E (2004), in press.
14. Baldovin F., Robledo A. Phys. Rev. E. 66:2002;045104(R) F. Baldovin, A. Robledo, cond-mat/0304410 Phys. Rev. E (2004), in press.
15. Baldovin F., Brigatti E., Tsallis C. Phys. Lett. A. 320:2004;254.
16. F. Baldovin, L.G. Moyano, A.P. Majtey, A. Robledo, C. Tsallis, Physica A (2004), these proceedings, doi: 10.1016/j.physa.2004.04.009.
17. G.F.J. Ananos, F. Baldovin, C. Tsallis, Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach, cond-mat/0403656.
18. Anteneodo C., Tsallis C. Phys. Rev. Lett. 80:1998;5313 Campa A., Giansanti A., Moroni D., Tsallis C. Phys. Lett. A. 286:2001;251 Cabral B.J.C., Tsallis C. Phys. Rev. E. 66:2002;065101(R) Nobre F.D., Tsallis C. Phys. Rev. E. 68:2003;036115 Borges E.P., Tsallis C., Giansanti A., Moroni D. Dinamica de um sistema nao extensivo de rotores classicos anisotropicos acoplados. Tome T. Tendencias da Fisica Estatistica no Brasil, volume honoring S.R.A. Salinas. 2003;84 Editora Livraria da Fisica, Sao Paulo.
19. Anteneodo C., Tsallis C. Phys. Rev. Lett. 80:1998;5313 Campa A., Giansanti A., Moroni D., Tsallis C. Phys. Lett. A. 286:2001;251 Cabral B.J.C., Tsallis C. Phys. Rev. E. 66:2002;065101(R) Nobre F.D., Tsallis C. Phys. Rev. E. 68:2003;036115 Borges E.P., Tsallis C., Giansanti A., Moroni D. Dinamica de um sistema nao extensivo de rotores classicos anisotropicos acoplados. Tome T. Tendencias da Fisica Estatistica no Brasil, volume honoring S.R.A. Salinas. 2003;84 Editora Livraria da Fisica, Sao Paulo.
20. Anteneodo C., Tsallis C. Phys. Rev. Lett. 80:1998;5313 Campa A., Giansanti A., Moroni D., Tsallis C. Phys. Lett. A. 286:2001;251 Cabral B.J.C., Tsallis C. Phys. Rev. E. 66:2002;065101(R) Nobre F.D., Tsallis C. Phys. Rev. E. 68:2003;036115 Borges E.P., Tsallis C., Giansanti A., Moroni D. Dinamica de um sistema nao extensivo de rotores classicos anisotropicos acoplados. Tome T. Tendencias da Fisica Estatistica no Brasil, volume honoring S.R.A. Salinas. 2003;84 Editora Livraria da Fisica, Sao Paulo.
21. Anteneodo C., Tsallis C. Phys. Rev. Lett. 80:1998;5313 Campa A., Giansanti A., Moroni D., Tsallis C. Phys. Lett. A. 286:2001;251 Cabral B.J.C., Tsallis C. Phys. Rev. E. 66:2002;065101(R) Nobre F.D., Tsallis C. Phys. Rev. E. 68:2003;036115 Borges E.P., Tsallis C., Giansanti A., Moroni D. Dinamica de um sistema nao extensivo de rotores classicos anisotropicos acoplados. Tome T. Tendencias da Fisica Estatistica no Brasil, volume honoring S.R.A. Salinas. 2003;84 Editora Livraria da Fisica, Sao Paulo.
22. Anteneodo C., Tsallis C. Phys. Rev. Lett. 80:1998;5313 Campa A., Giansanti A., Moroni D., Tsallis C. Phys. Lett. A. 286:2001;251 Cabral B.J.C., Tsallis C. Phys. Rev. E. 66:2002;065101(R) Nobre F.D., Tsallis C. Phys. Rev. E. 68:2003;036115 Borges E.P., Tsallis C., Giansanti A., Moroni D. Dinamica de um sistema nao extensivo de rotores classicos anisotropicos acoplados. Tome T. Tendencias da Fisica Estatistica no Brasil, volume honoring S.R.A. Salinas. 2003;84 Editora Livraria da Fisica, Sao Paulo.
23. Latora V., Baranger M., Rapisarda A., Tsallis C. Phys. Lett. A. 273:2000;97.
24. Lyra M.L., Tsallis C. Phys. Rev. Lett. 80:1998;53.
25. Montemurro M.A., Tamarit F., Anteneodo C. Phys. Rev. E. 67:2003;031106.
26. A. Robledo, cond-mat/0307285.
27. de Moura F.A.B.F., Tirnakli U., Lyra M.L. Phys. Rev. E. 62:2000;6361 Borges E.P., Tsallis C., Ananos G.F.J., Oliveira P.M.C. Phys. Rev. Lett. 89:2002;254103.
28. de Moura F.A.B.F., Tirnakli U., Lyra M.L. Phys. Rev. E. 62:2000;6361 Borges E.P., Tsallis C., Ananos G.F.J., Oliveira P.M.C. Phys. Rev. Lett. 89:2002;254103.
29. M. Planck, Verhandlungen der Deutschen Physikalischen Gessellschaft 2 (1900) 202 and 237, [English translation: D. ter Haar, S.G. Brush, Planck's Original Papers in Quantum Physics, Taylor and Francis, London, 1972].
30. M. Planck, Verhandlungen der Deutschen Physikalischen Gessellschaft 2 (1900) 202 and 237, [English translation: D. ter Haar, S.G. Brush, Planck's Original Papers in Quantum Physics, Taylor and Francis, London, 1972].
31. Latora V., Rapisarda A., Tsallis C. Phys. Rev. E. 64:2001;056134 Tsallis C., Rapisarda A., Latora V., Baldovin F. Dauxois T., Ruffo S., Arimondo E., Wilkens M. Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics. Vol. 602:2002;Springer, Berlin, A. Pluchino, V. Latora, A. Rapisarda, Spin-glass phase in the Hamiltonian Mean Field model, Physica A (2004), in press, cond-mat/0306374; C. Tsallis, What should a statistical mechanics satisfy to reflect nature?, in: H.L. Swinney, C. Tsallis (Eds.), Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, Physica D (2004), in press [cond-mat/0403012]; L.G. Moyano, F. Baldovin, C. Tsallis, cond-mat/0305091.
32. Latora V., Rapisarda A., Tsallis C. Phys. Rev. E. 64:2001;056134 Tsallis C., Rapisarda A., Latora V., Baldovin F. Dauxois T., Ruffo S., Arimondo E., Wilkens M. Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics. Vol. 602:2002;Springer, Berlin, A. Pluchino, V. Latora, A. Rapisarda, Spin-glass phase in the Hamiltonian Mean Field model, Physica A (2004), in press, cond-mat/0306374; C. Tsallis, What should a statistical mechanics satisfy to reflect nature?, in: H.L. Swinney, C. Tsallis (Eds.), Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, Physica D (2004), in press [cond-mat/0403012]; L.G. Moyano, F. Baldovin, C. Tsallis, cond-mat/0305091.
33. Latora V., Rapisarda A., Tsallis C. Phys. Rev. E. 64:2001;056134 Tsallis C., Rapisarda A., Latora V., Baldovin F. Dauxois T., Ruffo S., Arimondo E., Wilkens M. Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics. Vol. 602:2002;Springer, Berlin, A. Pluchino, V. Latora, A. Rapisarda, Spin-glass phase in the Hamiltonian Mean Field model, Physica A (2004), in press, cond-mat/0306374; C. Tsallis, What should a statistical mechanics satisfy to reflect nature?, in: H.L. Swinney, C. Tsallis (Eds.), Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, Physica D (2004), in press [cond-mat/0403012]; L.G. Moyano, F. Baldovin, C. Tsallis, cond-mat/0305091.
34. Latora V., Rapisarda A., Tsallis C. Phys. Rev. E. 64:2001;056134 Tsallis C., Rapisarda A., Latora V., Baldovin F. Dauxois T., Ruffo S., Arimondo E., Wilkens M. Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics. Vol. 602:2002;Springer, Berlin, A. Pluchino, V. Latora, A. Rapisarda, Spin-glass phase in the Hamiltonian Mean Field model, Physica A (2004), in press, cond-mat/0306374; C. Tsallis, What should a statistical mechanics satisfy to reflect nature?, in: H.L. Swinney, C. Tsallis (Eds.), Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, Physica D (2004), in press [cond-mat/0403012]; L.G. Moyano, F. Baldovin, C. Tsallis, cond-mat/0305091.
35. Latora V., Rapisarda A., Tsallis C. Phys. Rev. E. 64:2001;056134 Tsallis C., Rapisarda A., Latora V., Baldovin F. Dauxois T., Ruffo S., Arimondo E., Wilkens M. Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics. Vol. 602:2002;Springer, Berlin, A. Pluchino, V. Latora, A. Rapisarda, Spin-glass phase in the Hamiltonian Mean Field model, Physica A (2004), in press, cond-mat/0306374; C. Tsallis, What should a statistical mechanics satisfy to reflect nature?, in: H.L. Swinney, C. Tsallis (Eds.), Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, Physica D (2004), in press [cond-mat/0403012]; L.G. Moyano, F. Baldovin, C. Tsallis, cond-mat/0305091.
36. Mendes R.S., Tsallis C. Phys. Lett. A. 285:2001;273.
37. Albert R., Barabasi A.L. Phys. Rev. Lett. 85:2000;5234.