Nonanalytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable one-dimensional model for evaporation

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

Volumn 74, Issue 1, 2006, Pages

  Hilbert, Stefan ^a   Dunkel, Jörn ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; MATHEMATICAL MODELS; MICROSCOPIC EXAMINATION; OSCILLATIONS; PHASE TRANSITIONS; SPECIFIC HEAT; THERMAL EFFECTS; THERMODYNAMICS;

MICROCANONICAL ENSEMBLES; MICROSCOPIC PHASE TRANSITIONS; TEMPERATURE INDUCED DISSOCIATION; THERMODYNAMIC FUNCTIONS (TDF);

EVAPORATION;

EID: 33746618476     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.011120     Document Type: Article

References (47)

1. L. P. Kadanoff, W. Götze, D. Hamblen, R. Hecht, E. A. S. Lewis, V. V. Palciauskas, M. Rayl, J. Swift, D. Aspnes, and J. Kane, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.39.395 39, 395 (1967).
2. L. D. Landau and E. M. Lifshitz, Statistical Physics, Vol. 5 of Course of Theoretical Physics, 3rd ed. (Butterworth-Heinemann, Oxford, 2003).
3. J. E. Mayer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1749933 5, 67 (1937).
4. J. E. Mayer and P. G. Ackermann, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1749934 5, 74 (1937).
5. S. F. Streeter and J. E. Mayer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1750361 7, 1025 (1939).
6. L. Onsager, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.65.117 65, 117 (1944).
7. L. van Hove, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/0031-8914(50) 90072-3 16, 137 (1950).
8. C. N. Yang and T. D. Lee, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.87.404 87, 404 (1952).
9. T. D. Lee and C. N. Yang, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.87.410 87, 410 (1952).
10. M. E. Fisher, in Critical Phenomena: Proceedings of the 51st Enrico Fermi Summer School, Varenna, Italy, edited by, M. S. Green, (Academic Press, New York, 1971), p. 1.
11. S. Grossmann and W. Rosenhauer, Z. Phys. ZEPYAA 0044-3328 207, 138 (1967).
12. S. Grossmann and W. Rosenhauer, Z. Phys. ZEPYAA 0044-3328 218, 437 (1969).
13. S. Grossmann and V. Lehmann, Z. Phys. ZEPYAA 0044-3328 218, 449 (1969).
14. T. W. Burkhardt, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/14/3/003 14, L63 (1981).
15. L. Casetti, E. G. D. Cohen, and M. Pettini, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036112 65, 036112 (2002).
16. R. Franzosi and M. Pettini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.060601 92, 060601 (2004).
17. L. Angelani, L. Casetti, M. Pettini, G. Ruocco, and F. Zamponi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.036152 71, 036152 (2005).
18. J. A. Cuesta and A. Sánchez, J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000022373.63640.4e 115, 869 (2004).
19. D. Ruelle, Statistical Mechanics (World Scientific, Singapore, 1999).
20. P. Borrmann, O. Mülken, and J. Harting, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3511 84, 3511 (2000).
21. O. Mülken, H. Stamerjohanns, and P. Borrmann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.047105 64, 047105 (2001).
22. W. Janke and R. Kenna, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1004836227767 102, 1211 (2001).
23. N. A. Alves, J. P. N. Ferrite, and U. H. E. Hansmann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036110 65, 036110 (2002).
24. D. J. Wales and R. S. Berry, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.2875 73, 2875 (1994).
25. D. J. Wales and J. P. K. Doye, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.470494 103, 3061 (1995).
26. D. H. E. Gross, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(96)00024-5 279, 119 (1997).
27. D. H. E. Gross, Micro-Canonical Thermodynamics, Vol. 66 of World Scientific Lecture Notes in Physics (World Scientific, Singapore, 2001).
28. M. Costeniuc, R. S. Ellis, H. Touchette, and B. Turkington, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-005-4407-0 119, 1283 (2005).
29. P. Chomaz, V. Duflot, and F. Gulminelli, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3587 85, 3587 (2000).
30. J. Dunkel and S. Hilbert, e-print cond-mat/0511501, Physica A (to be published).
31. P. Hertz, Ann. Phys. ANPYA2 0003-3804 33, 225 (1910).
32. P. Hertz, Ann. Phys. ANPYA2 0003-3804 33, 537 (1910).
33. R. Becker, Theory of Heat (Springer, New York, 1967).
34. K. Huang, Statistical Mechanics (Wiley, New York, 1963).
35. A. Münster, Statistical Thermodynamics, Vol. 1 (Springer, Berlin, 1969).
36. P. Ehrenfest and T. Ehrenfest, The Conceptual Foundation of the Statistical Approach In Mechanics (Cornell University Press, Ithaca, NY, 1959), reprint of german 1912 edition.
37. P. Ehrenfest, Proc. R. Acad. Sci. Amsterdam PKNAAU 0370-0348 36, 153 (1933).
38. M. Kastner and O. Schnetz, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-005-8031-9 122, 1195 (2006).
39. D. H. E. Gross, e-print cond-mat/0403582.
40. J. P. K. Doye, Ph.D. thesis, Gonville & Caius College, University of Cambridge, UK, 1996.
41. M. Schmidt, T. Hippler, J. Donges, W. Kronmüller, B. von Issendorff, H. Haberland, and P. Labastie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.203402 87, 203402 (2001).
42. O. S. Vaulina, S. V. Vladimirov, O. F. Petrov, and V. E. Fortov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.245002 88, 245002 (2002).
43. F. Schwabl, Statistische Mechanik (Springer, New York, 2000) (in German).
44. E. M. Pearson, T. Halicioglu, and W. A. Tiller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.3030 32, 3030 (1985).
45. O. Mülken, Ph.D. thesis, Universität Oldenburg, Germany, 2001.
46. M. Kastner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93. 150601 93, 150601 (2004).
47. A. C. Ribeiro Teixeira and D. A. Stariolo, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.016113 70, 016113 (2004).