Linear response theory for thermodynamic properties

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 1, 1999, Pages 471-481

  Nielsen, Johannes K ^a  

^a ROSKILDE UNIVERSITY   (Denmark)

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ARTICLE;

EID: 0004375587     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.471     Document Type: Article

References (43)

1. W. W. Van Osdol, R. L. Biltonen, and Michael L. Johnson, J. Biochem. Biophys. Methods 20, 1 (1989).
2. T. Christensen, J. Phys. (Paris), Colloq. 46, C8-635 (1985).
3. N. O. Birge and S. R. Nagel, Phys. Rev. Lett. 54, 2674 (1985).
4. P. K. Dixon and S. R. Nagel, Phys. Rev. Lett. 61, 341 (1988)
5. P. K. Dixon, Phys. Rev. B 42, 8179 (1990).
6. N. Menon, J. Chem. Phys. 105, 5246 (1996).
7. T. Christensen and N. B. Olsen, Phys. Rev. B 49, 15 396 (1994).
8. J. Jäckle, Z. Phys. B 64, 41 (1986).
9. J. Jäckle, Physica A 162, 377 (1990).
10. W. Götze and A. Latz, J. Phys.: Condens. Matter 1, 4169 (1989).
11. R. Zwanzig, J. Chem. Phys. 88, 5831 (1988).
12. D. W. Oxtoby, J. Chem. Phys. 85, 1549 (1986).
13. M. Cieplak and G. Szamel, Phys. Rev. B 37, 1790 (1988).
14. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)
15. J. Phys. Soc. Jpn.R. Kubo12, 1203 (1957).
16. N. G. van Kampen, Phys. Norv. 5, 279 (1971).
17. In Ref. 14 the linear assumption used in Ref. 13 is shown to be wrong, essentially because a realistic system cannot be linear in the force (Formula presented) at a microscopic level, due to the chaotic nature of the phase space trajectories. In the linear response scheme developed in the present paper the linearization is introduced solely by the construction of the initial distribution Eq. (21), while the time evolution of the phase space probability is evaluated from unperturbed (autonomous), Hamiltonian or general stochastic dynamics, thus avoiding the assumption of microscopic linearity.
18. J. K. Nielsen and J. C. Dyre, Phys. Rev. B 54, 15 754 (1996).
19. N. G. Van Kampen, Stochastic Processes In Physics and Chemistry (North-Holland, Amsterdam, 1981).
20. W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995)
21. Phys. Rev. EW. KobH. C. Andersen52, 4134 (1995).
22. S.-H. Chen, P. Gallo, F. Sciortino, and P. Tartaglia, Phys. Rev. E 56, 4231 (1997).
23. J. L. Lebowitz, J. K. Percus, and L. Verlet, Phys. Rev. 153, 250 (1967).
24. J. R. Ray and H. W. Graben, Mol. Phys. 43, 1293 (1981)
25. Mol. Phys.P. S. Y. Cheung, 33, 519 (1977).
26. G. S. Grest and S. R. Nagel, J. Phys. Chem. 91, 4916 (1987).
27. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 2nd ed. (Academic, London, 1991), p. 230.
28. D. Ronis and I. Oppenheim, Physica A 86, 475 (1977).
29. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford Science Publications, Oxford, 1994).
30. A proper dynamic definition of temperature should at least give exactly the microcanonical temperature (Formula presented) when averaged 27. This is why the number of kinetic degrees of freedom becomes important. However, it is unclear exactly how much the number of kinetic degrees of freedom is reduced by the isoenergetic constraint, except that it must be a number around 1, depending on the potential.
31. H. H. Rugh, Phys. Rev. Lett. 78, 772 (1997)
32. H. H. RughJ. Phys. A: Math. Gen. 31, 7761 (1998).
33. T. E. Christensen (unpublished).
34. The parameter (Formula presented) is in Ref. 18 set to (Formula presented). The reason that it is set to (Formula presented) here is a programming error.
35. A first order linearization of the Hamiltonian equations of motion is used.
36. D. J. Evans and B. L. Holian, J. Chem. Phys. 83, 4069 (1985)
37. S. Nosé, Prog. Theor. Phys. Suppl. 103, 1 (1991).
38. Engineering and Scientific Subroutine Library, Version 2, Release 2, IBM Corporation, 1994.
39. G. Williams and D. C. Watts, Trans. Faraday Soc. 65, 80 (1969).
40. C. A. Angell, Science 267, 1924 (1995).
41. H. Leyser, A. Shulte, W. Doster, and W. Petry, Phys. Rev. E 51, 5899 (1995).
42. C. A. Angell and K. J. Rao, J. Chem. Phys. 57, 470 (1972).
43. P. Scheilder, W. Kob, J. Horbach, and K. Binder, cond-mat/9901089, 1999 (unpublished).