Non-equilibrium critical behavior: An extended irreversible thermodynamics approach

Journal of Non-Equilibrium Thermodynamics

Volumn 31, Issue 4, 2006, Pages 397-417

  Hernández Lemus, Enrique ^a   García Colín, Leopoldo S ^b,c  

^a Universidad Nacional Autonoma de Mexico Facultad de Quimica   (Mexico)

^b DEPARTAMENTO DE QUÍMICA   (Mexico)

^c EL COLEGIO NACIONAL   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; NEUTRON SCATTERING; OPTICAL CORRELATION; PHASE TRANSITIONS; X RAY DIFFRACTION ANALYSIS;

DIAGRAMMATIC TECHNIQUES; DYNAMIC PHASE TRANSITIONS; IRREVERSIBLE THERMODYNAMICS;

THERMODYNAMICS;

ALGEBRA; NEUTRON SCATTERING; OPTICAL CORRELATION; PHASE TRANSITIONS; THERMODYNAMICS; X RAY DIFFRACTION ANALYSIS;

EID: 33751533716     PISSN: 03400204     EISSN: 14374358     Source Type: Journal    
DOI: 10.1515/JNETDY.2006.017     Document Type: Article

References (53)

1. Binney, J. et al., The theory of critical phenomena, Oxford Science, New York, 1992.
2. Stanley, H.E., Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, London, 1971.
3. Griffiths, R.B., Wheeler, J.C., Critical points in multicomponent systems, Phys. Rev. A, 2 (1970), 1047-1064.
4. Widom, B., Surface tension and molecular correlations near the critical point, J. Chem. Phys. 43, 11 (1965), 3892-3897.
5. Ruppeiner, G., Riemannian geometric theory of critical phenomena, Phys. Rev. A, 44 (1991), 3583-3595;
6. Ibid., Asymmetric free energy from Riemannian geometry, Phys. Rev. E, 47 (1993), 934-938;
7. Riemannian geometric approach to critical points: general theory, Phys. Rev. E, 57 (1998), 5135-5145
8. and Riemannian geometry in thermodynamic fluctuation theory, Rev. Mod. Phys., 67 (1995), 605-659.
9. Fixman, M., Viscosity of critical mixtures, J. Chem. Phys., 36 (1962), 310-318.
10. Kawasaki, K., Kinetics of Ising Models, in: Phase Transitions and Critical Phenomena, vol. 2, pp. 443-501, Eds. C. Domb and M.S. Green, Academic Press, New York, 1972.
11. Hohenberg, P., Halperin, B.I., Theory of dynamic critical phenomena, Rev. Mod. Phys. 49 (1977), 435-479.
12. Halperin, B.I., Hohenberg, P.C., Scaling Laws for Dynamic Critical Phenomena, Phys. Rev., 177 (1969), 952-971.
13. Gunton, J.D., in: Dynamical Critical Phenomena and Related Topics, Ed. C.P. Enz, Springer, New York, 1979.
14. García-Colín, L.S., On the macroscopic derivation of mode-mode coupling equations, J. Stat. Phys. 20 (1979), 19-24.
15. Burstyn, H.C., Sengers, J.V., et al., Dynamic scaling function for critical fluctuations in classical fluids, Phys. Rev. A, 28 (1983), 1567-1578.
16. Burstyn, H.C., Sengers, J.V., Time dependence of critical concentration fluctuations in a binary liquid, Phys. Rev. A, 27 (1983), 1071-1085.
17. Chang, R.F., Burstyn, H.C., Sengers, J.V., Correlation function near the critical mixing point of a binary liquid, Phys. Rev. A, 19 (1979), 866-882.
18. Burstyn, H.C., Sengers, J.V., Esfandiari, P., Stokes-Einstein diffusion of critical fluctuations in a fluid, Phys. Rev. A, 22 (1980), 282-284.
19. Boon, J.P., Yip, S., Molecular Hydrodynamics, Dover, New York, 1991.
20. García-Colín, L.S., Uribe, F.J., Extended irreversible thermodynamics beyond the linear regime: a critical overview, J. Non-Equilib. Thermodyn., 16 (1991), 89-128.
21. Jou, D., Casas-Vázquez, J., Lebon, G., Extended Irreversible Thermodynamics, Springer, Berlin, 1993.
22. García-Colín, L.S., Rodríguez, R.F., López de Haro, M., Jou, D., Pérez García, C., Generalized hydrodynamics and extended irreversible thermodynamics, Phys. Rev. A, 31 (1985), 2502-2508.
23. Chen, M., Eu, B.C., On the integrability of differential forms related to non-equilibrium entropy and irreversible thermodynamics, J. Math. Phys., 34 (1993), 3012-3029.
24. Eu, B.C., Form of uncompensated heat giving rise to a Pfaffian differential form in thermodynamic space, Phys. Rev. E, 51 (1995), 768-771.
25. Bhalekar, A., García-Colín, L.S., On the construction of an extended thermodynamic framework for irreversible processes, Pramana, J. Physics (India), 50 (1998), 295-305.
26. Cattaneo, C., Sulla conduzione del calore, Atti del Seminario Matematico e Fisico dell'Università di Modena, 3 (1949), 83-101.
27. Vernotte, P., Les paradoxes de la théorie continue de l'équation de la chaleur, Compte Rendus, 246 (1958), 3154-3155.
28. Lebon, G., Casas-Vázquez, J., Towards a thermodynamic theory of the third type, in: Thermodynamics History and Philosophy, Eds. K. Martinás, L. Ropolyi, P. Szegedi, World Scientific, Singapore, 1990.
29. Muschik, W., Fundamentals of nonequilibrium thermodynamics, in: Non-Equilibrium Thermodynamics with Applications to Solids, Section 1, p. 1-63 (CISM Courses and Lectures 336), Ed. W. Muschik, Springer, Vienna, 1993.
30. Muschik, W., Aspects of Non-Equilibrium Thermodynamics, World Scientific, Singapore, 1990.
31. Muschik, W., Recent Developments in Non-Equilibrium Thermodynamics, (Lecture Notes in Physics 199), p. 387, Springer, Berlin, 1984.
32. Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, John Wiley and Sons, New York, 1985.
33. Tisza, L., Generalized Thermodynamics, MIT Press, Cambridge, Mass., 1966.
34. Meixner, J., On the foundations of thermodynamics of processes, in: A Critical Review of Thermodynamics, Ed. E.B. Stuart, Mono Book, Baltimore, 1970.
35. Eu, B.C., Kinetic Theory and Irreversible Thermodynamics, J. Wiley, New York, 1992.
36. García-Colín, L.S., Introducción a la Termodinámica Clásica (in Spanish), Trillas, México, 1995. See chapter 14 or any other book on classical thermodynamics treating the scaling theory of critical exponents.
37. Zwanzig, R., Memory effects in irreversible thermodynamics, Phys. Rev., 124 (1961), 983-992.
38. van Kampen, N., Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam, 1992.
39. Martin, N., England, J.W., Mathematical Theory of Entropy, Adison-Wesley, London, 1981.
40. Zubarev, D.N., Morozov, V., Röpke, G., Statistical Mechanics of Nonequilibrium Processes, Akademie Verlag, Berlin, 1996.
41. Zubarev, D.N., Nonequilibrium Statistical Thermodynamics, Trans. P.J. Shepherd, Eds. P. Gray, P.J. Shepherd, Consultants Bureau, New York, 1974.
42. Harris, R., Hurley, J., Garrod, C., Nonequilibrium ensemble dynamics, Phys. Rev. A, 41 (1987), 1350-1359.
43. Mirzaev, S.Z., Kaatze, U., Critical concentration fluctuations of the ionic binary mixture ethylammonium nitrate-n-octanol: an ultrasonic spectrometry study, Phys. Rev. E, 65 (2002), 1-6.
44. Dufresne, E., Nurushev, T., Clarke, R., Dierker, S.B., A study of concentration fluctuations in the binary mixture hexane-nitrobenzene with X-ray photon correlation spectroscopy. Department of Physics, University of Michigan, Ann Arbor, Michigan.
45. Fine, B.M., et al., Dynamic critical phenomena in aqueous protein solutions, Phys. Rev. Lett., 74 (1995), 198-201.
46. Gradshtein, I.S., Ryzhik, I.M., Table of Integrals, Series, and Products, Academic Press, New York, 1980.
47. Martin, A., Casielles, A.G., et al., Two-exponential correlation functions near the critical point of a micellar system, Phys. Rev. E, 58 (1998), 2151-2160.
48. Campostrini, M., Pelissetto, A., Rossi, P., Vicari, E., 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice, Phys. Rev. E, 65 (2002), 1-19.
49. Campostrini, M., Pelissetto, A., Rossi, P., Vicari, E., Improved high-temperature expansion and critical equation of state of three-dimensional Isinglike systems, Phys. Rev E, 60 (1999), 3526-3563.
50. Berg, R.F., Moldover, M.R., Zimmerli, G.A., Viscoelasticity of xenon near the critical point, Phys. Rev. Lett., 82 (1999), 920-923.
51. Guida, R., Zinn-Justin, J., Critical exponents of the N-vector model, J. Phys. A, Math. Gen., 31 (1998), 8103-8121.
52. Hao, H., Ferrel, R.A., Bhattacharjee, J.K., Critical viscosity exponent for classical fluids, Phys. Rev. E, 71 (2005), 1-12.
53. Oh, J., Órtiz de Zarate, J.M., Sengers, J.V., Ahlers, G., Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection, Phys. Rev. E, 69 (2004), 1-13.