Comment on "critique of q-entropy for thermal statistics"

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 69, Issue 3 2, 2004, Pages

  Tsallis, C ^a,b  

^a CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

^b SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; DEGREES OF FREEDOM (MECHANICS); DIFFUSION; ENTROPY; FERROMAGNETISM; GIBBS FREE ENERGY; HAMILTONIANS; KINETIC ENERGY; POTENTIAL ENERGY; PROBABILITY; PROBLEM SOLVING; SENSITIVITY ANALYSIS; THERMODYNAMICS; VELOCITY MEASUREMENT;

MOLECULAR CHAOS HYPOTHESIS; STANDARD EXPECTATIONS; THERMAL EQUILIBRIUM; THERMAL STATISTICS;

STATISTICAL MECHANICS;

EID: 23244442683     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.69.038101     Document Type: Review

References (47)

1. M. Nauenberg, Phys. Rev. E 67, 036114 (2003).
2. M.E. Fisher, Arch. Ration. Alech. Anal. 17, 377 (1964); J. Chem. Phys. 42, 3852 (1965); J. Math. Phys. 6, 1643 (1965); M.E. Fisher and D. Ruelle, ibid. 7, 260 (1966); M.E. Fisher and J.L. Lebowitz, Commun. Math. Phys. 19, 251 (1970).
3. M.E. Fisher, Arch. Ration. Alech. Anal. 17, 377 (1964); J. Chem. Phys. 42, 3852 (1965); J. Math. Phys. 6, 1643 (1965); M.E. Fisher and D. Ruelle, ibid. 7, 260 (1966); M.E. Fisher and J.L. Lebowitz, Commun. Math. Phys. 19, 251 (1970).
4. M.E. Fisher, Arch. Ration. Alech. Anal. 17, 377 (1964); J. Chem. Phys. 42, 3852 (1965); J. Math. Phys. 6, 1643 (1965); M.E. Fisher and D. Ruelle, ibid. 7, 260 (1966); M.E. Fisher and J.L. Lebowitz, Commun. Math. Phys. 19, 251 (1970).
5. M.E. Fisher, Arch. Ration. Alech. Anal. 17, 377 (1964); J. Chem. Phys. 42, 3852 (1965); J. Math. Phys. 6, 1643 (1965); M.E. Fisher and D. Ruelle, ibid. 7, 260 (1966); M.E. Fisher and J.L. Lebowitz, Commun. Math. Phys. 19, 251 (1970).
6. M.E. Fisher, Arch. Ration. Alech. Anal. 17, 377 (1964); J. Chem. Phys. 42, 3852 (1965); J. Math. Phys. 6, 1643 (1965); M.E. Fisher and D. Ruelle, ibid. 7, 260 (1966); M.E. Fisher and J.L. Lebowitz, Commun. Math. Phys. 19, 251 (1970).
7. V. Latora, A. Rapisarda, and C. Tsallis, Phys. Rev. E 64, 056134 (2001); also see F.D. Nobre and C. Tsallis, ibid. 68, 036115 (2003); C. Tsallis, in Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann and C. Tsallis (Oxford University Press, New York, 2004).
8. V. Latora, A. Rapisarda, and C. Tsallis, Phys. Rev. E 64, 056134 (2001); also see F.D. Nobre and C. Tsallis, ibid. 68, 036115 (2003); C. Tsallis, in Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann and C. Tsallis (Oxford University Press, New York, 2004).
9. V. Latora, A. Rapisarda, and C. Tsallis, Phys. Rev. E 64, 056134 (2001); also see F.D. Nobre and C. Tsallis, ibid. 68, 036115 (2003); C. Tsallis, in Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann and C. Tsallis (Oxford University Press, New York, 2004).
10. E. Fermi, Thermodynamics (Dover, New York, 1936) ["The entropy of a system composed of several parts is very often equal to the sum of the entropies of all the parts, This is true if the energy of the system is the sum of the energies of all the parts and if the work performed by the system during a transformation is equal to the sum of the amounts of work performed by all the parts. Notice that these conditions are not quite obvious and that in some cases they may not be fulfilled. Thus, for example, in the case of a system composed of two homogeneous substances, it will be possible to express the energy as the sum of the energies of the two substances only if we can neglect the surface energy of the two substances where they are in contact. The surface energy can generally be neglected only if the two substances are not very finely subdivided; otherwise, it can play a considerable role."].
11. C. Tsallis, A.R. Plastino, and W.-M. Zheng, Chaos, Solitons Fractals 8, 885 (1997).
12. U.M.S. Costa, M.L. Lyra, A.R. Plastino, and C. Tsallis, Phys. Rev. E 56, 245 (1997).
13. M.L. Lyra and C. Tsallis, Phys. Rev. Lett. 80, 53 (1998).
14. F.A.B.F. de Moura, U. Tirnakli, and M.L. Lyra, Phys. Rev. E 62, 6361 (2000).
15. E.P. Borges, C. Tsallis, G.F.J. Ananos, and P.M.C. Oliveira, Phys. Rev. Lett. 89, 254103 (2002).
16. F. Baldovin and A. Robledo, Europhys. Lett. 60, 518 (2002).
17. F. Baldovin and A. Robledo, Phys. Rev. E 66, 045104(R) (2002).
18. A. Plastino, Science 300, 250 (2003).
19. V. Latora, A. Rapisarda, and A. Robledo, Science 300, 250 (2003).
20. G.A. Tsekouras, A. Provata, and C. Tsallis, Phys. Rev. E 69, 016120 (2004); B.M. Boghosian, P.J. Love, P.V. Coveney, I.V. Karlin, S. Succi, and J. Yepez, Phys. Rev. E 68, 025103 (2003); B.M. Boghosian, P.J. Love, J. Yepez, and P.V. Coveney, in Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, edited by H. L. Swinney and C. Tsallis, (Elsevier, Amsterdam, in press).
21. G.A. Tsekouras, A. Provata, and C. Tsallis, Phys. Rev. E 69, 016120 (2004); B.M. Boghosian, P.J. Love, P.V. Coveney, I.V. Karlin, S. Succi, and J. Yepez, Phys. Rev. E 68, 025103 (2003); B.M. Boghosian, P.J. Love, J. Yepez, and P.V. Coveney, in Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, edited by H. L. Swinney and C. Tsallis, (Elsevier, Amsterdam, in press).
22. G.A. Tsekouras, A. Provata, and C. Tsallis, Phys. Rev. E 69, 016120 (2004); B.M. Boghosian, P.J. Love, P.V. Coveney, I.V. Karlin, S. Succi, and J. Yepez, Phys. Rev. E 68, 025103 (2003); B.M. Boghosian, P.J. Love, J. Yepez, and P.V. Coveney, in Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, edited by H. L. Swinney and C. Tsallis, (Elsevier, Amsterdam, in press).
23. C. Anteneodo and C. Tsallis, Phys. Rev. Lett. 80, 5313 (1998).
24. A. Campa, A. Giansanti, D. Moroni, and C. Tsallis, Phys. Lett. A 286, 251 (2001).
25. B.J.C. Cabrai and C. Tsallis, Phys. Rev. E 66, 065101 (R) (2002).
26. M.A. Montemurro, F. Tamarit, and C. Anteneodo, Phys. Rev. E 67, 031106 (2003); A. Pluchino, V. Latora, and A. Rapisarda, in Anomalous Distributions, Nonlinear Dynamics and Nonextensivity (Ref. [14]).
27. M.A. Montemurro, F. Tamarit, and C. Anteneodo, Phys. Rev. E 67, 031106 (2003); A. Pluchino, V. Latora, and A. Rapisarda, in Anomalous Distributions, Nonlinear Dynamics and Nonextensivity (Ref. [14]).
28. C. Tsallis, A. Rapisarda, V. Latora, and F. Baldovin, in Dynamics and Thermodynamics of Systems with Long Range Interactions, edited by T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens, Lecture Notes in Physics, Vol. 602 (Springer, Berlin, 2002).
29. J.P.K. Doye, Phys. Rev. Lett. 88, 238701 (2002).
30. R. Albert and A.L. Barabasi, Phys. Rev. Lett. 85, 5234 (2000).
31. F. Baldovin, E. Brigatti, and C. Tsallis, Phys. Lett. A 320, 254 (2004).
32. A. Campa, A. Giansanti, and D. Moroni, Physica A 305, 137 (2002).
33. A.C.D. van Enter, R. Fernandez, and A.D. Sokal, J. Stat. Phys. 72, 879 (1993).
34. S. Abe and A.K. Rajagopal, J. Phys. A 33, 8733 (2000); Europhys. Lett. 52, 610 (2000); Phys. Lett. A 272, 341 (2000); Europhys. Lett. 55, 6 (2001).
35. S. Abe and A.K. Rajagopal, J. Phys. A 33, 8733 (2000); Europhys. Lett. 52, 610 (2000); Phys. Lett. A 272, 341 (2000); Europhys. Lett. 55, 6 (2001).
36. S. Abe and A.K. Rajagopal, J. Phys. A 33, 8733 (2000); Europhys. Lett. 52, 610 (2000); Phys. Lett. A 272, 341 (2000); Europhys. Lett. 55, 6 (2001).
37. S. Abe and A.K. Rajagopal, J. Phys. A 33, 8733 (2000); Europhys. Lett. 52, 610 (2000); Phys. Lett. A 272, 341 (2000); Europhys. Lett. 55, 6 (2001).
38. S. Abe and A.K. Rajagopal, Science 300, 249 (2003).
39. R.J.V. Santos, J. Math. Phys. 38, 4104 (1997); S. Abe, Phys. Lett. A 271, 74 (2000).
40. R.J.V. Santos, J. Math. Phys. 38, 4104 (1997); S. Abe, Phys. Lett. A 271, 74 (2000).
41. S. Abe, Phys. Rev. E 66, 046134 (2002).
42. V. Latora, M. Baranger, A. Rapisarda, and C. Tsallis, Phys. Lett. A 273, 97 (2000). Also see the q generalization of Pesin theorem, conjectured in Ref. [5], and recently proved for a large class of nonlinear dynamical systems by F. Baldovin and A. Robledo, preprint cond-mat/0304410.
43. L.G. Moyano, F. Baldovin, and C. Tsallis, preprint, cond-mat/0305091.
44. C. Tsallis and A.M.C. Souza, Phys. Rev. E 67, 026106 (2003); A.M.C. Souza and C. Tsallis, Phys. Lett. A 319, 273 (2003).
45. C. Tsallis and A.M.C. Souza, Phys. Rev. E 67, 026106 (2003); A.M.C. Souza and C. Tsallis, Phys. Lett. A 319, 273 (2003).
46. C. Beck and E.G.D. Cohen, Physica A 321, 267 (2003).
47. S. Abe and A.K. Rajagopal, Phys. Rev. Lett. 91, 120601 (2003).