Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic, and conservative interactions
| dc.contributor.author | Ernst, M. H. | |
| dc.contributor.author | Brito López, Ricardo | |
| dc.date.accessioned | 2023-06-20T10:34:54Z | |
| dc.date.available | 2023-06-20T10:34:54Z | |
| dc.date.issued | 2005-12 | |
| dc.description | ©2005 The American Physical Society. M.H.E. is supported by Secretaría de Estado de Educación y Universidades (Spain), and R.B. by the Universidad Complutense (Profesores en el Extranjero). This work is financed by the research project FIS2004-271 (Spain). | |
| dc.description.abstract | We present a generalization of the Green-Kubo expressions for thermal transport coefficients mu in complex fluids of the generic form mu=mu(infinity)+integral(infinity)(0) dtV(-1)< J(epsilon)exp(tL)J >(0), i.e. a sum of an instantaneous transport coefficient mu(infinity), and a time integral over a time correlation function in a state of thermal equilibrium between a current J and its conjugate current J(epsilon). The streaming operator exp(tL) generates the trajectory of a dynamical variable J(t)=exp(tL)J when used inside the thermal average <(...)>(0). These formulas are valid for conservative, impulsive (hard spheres), stochastic, and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general mu(infinity)not equal 0 and J(epsilon)not equal J, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid. | |
| dc.description.department | Depto. de Estructura de la Materia, Física Térmica y Electrónica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Secretaría de Estado de Educación y Universidades (Spain) | |
| dc.description.sponsorship | Universidad Complutense (Profesores en el Extranjero) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21348 | |
| dc.identifier.doi | 10.1103/PhysRevE.72.061102 | |
| dc.identifier.issn | 1539-3755 | |
| dc.identifier.officialurl | http://pre.aps.org/pdf/PRE/v72/i6/e061102 | |
| dc.identifier.relatedurl | http://pre.aps.org/ | |
| dc.identifier.relatedurl | http://igitur-archive.library.uu.nl/phys/2006-1125-200635/ernst_05_generalized.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50640 | |
| dc.issue.number | 6, Par | |
| dc.journal.title | Physical Review E | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | FIS2004-271 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 536 | |
| dc.subject.keyword | Modified enskog equation | |
| dc.subject.keyword | Gas cellular automata | |
| dc.subject.keyword | Hard-sphere fluid | |
| dc.subject.keyword | Particle dynamics | |
| dc.subject.keyword | Energy-conservation | |
| dc.subject.keyword | Hydrodynamics | |
| dc.subject.keyword | Scale | |
| dc.subject.ucm | Termodinámica | |
| dc.subject.unesco | 2213 Termodinámica | |
| dc.title | Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic, and conservative interactions | |
| dc.type | journal article | |
| dc.volume.number | 72 | |
| dcterms.references | 1. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Wiley, New York, 1986). 2. M. P. Allen and D. J. Tildesley, Computer Simulations in Liquids (Wiley, New York, 1987). 3. M. H. Ernst and J. R. Dorfman, J. Stat. Phys. 12, 311 (1975). 4. For a dissident’s voice, see N. G. van Kampen, Phys. Norv. 5, 278 (1971). 5. M. H. Ernst and R. Brito, Europhys. Lett. (to be published). 6. M. H. Ernst (in preparation). 7. J. W. Dufty and M. H. Ernst, Mol. Phys. 102, 2123 (2004). 8. J. Piasecki, L. Bouquet, and J-P Hansen, J. Stat. Phys. 76, 505 (1994); Physica A 218, 125 (1995). 9. M. H. Ernst and J. W. Dufty, Phys. Lett. A 138, 391 (1989); J. W. Dufty and M. H. Ernst, J. Phys. Chem. 93, 7015 (1989). 10. T. Ihle and D. M. Kroll, Phys. Rev. E 67, 066705 (2003); 67, 066706 (2003). 11. P. J. Hoogerbrugge and J. M. V. A. Koelman, Europhys. Lett. 19, 191 (1995). 12. P. Español and P. Warren, Europhys. Lett. 56, 1676 (1997). 13. C. A. Marsh, G. Backx, and M. H. Ernst, Phys. Rev. E 56, 1676 (1997). 14. P. Español, Phys. Rev. E 52, 1734 (1995). 15. M. Ripoll and M. H. Ernst, Phys. Rev. E 71, 041104 (2005). 16. H. C. Oettinger, Beyond Equilibrium Thermodynamics (Wiley-Interscience, New York, 2005). 17. S. Hess, M. Kröger, and D. Evans, Phys. Rev. E 67, 042201 (2003). 18. V. Romero-Rochín and J. M. Rubí, Phys. Rev. E 58, 1843 (1998). 19. J. Bonet-Avalos and A. D. Mackie, Europhys. Lett. 40, 141 (1997). 20. P. Español, Europhys. Lett. 40, 631 (1997). 21. P. Español and M. Revenga, Phys. Rev. E 67, 026705 (2003). 22. M. Ripoll, M. H. Ernst, and P. Español, J. Chem. Phys. 15, 7271 (2001). 23. P. Español and F. Vázquez, Proc. R. Soc. London, Ser. A 360,383 (2002). 24. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977). 25. I. Goldhirsch and T. P. C. van Noije, Phys. Rev. E 61, 3241 (2000). 26. J. Dufty and A. Baskaran, cond-mat/0507609. (their L=L+ and their L¯ =L¯− in the standard notation of hard sphere kinetic theory). 27. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1996). 28. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983). 29. The unconventional notation of writing the Fokker-Planck operator L as a transpose was chosen here to unify the notation for the time dependence of dynamical variables in the form A(t)=expt[tL]A(0), both for mesoscopic variables (Fokker-Planck equation), as well as for microscopic ones (Hamilton and Liouville equations). 30. M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen, Physica (Utrecht) 45, 127 (1969). 31. H. van Beijeren and M. H. Ernst, J. Stat. Phys. 21, 125 (1979). 32. I. M. de Schepper, M. H. Ernst, and E. G. D. Cohen, J. Stat. Phys. 25, 321 (1981). 33. P. Resibois and M. de Leener, Classical Kinetic Theory of Liquids (Wiley, New York, 1997). 34. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, 1970). 35. H. van Beijeren and M. H. Ernst, Physica (Amsterdam) 68, 437 (1973); 70, 225 (1973). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | b5d83e4b-6cf5-4cfc-9a1e-efbf55f71f87 | |
| relation.isAuthorOfPublication.latestForDiscovery | b5d83e4b-6cf5-4cfc-9a1e-efbf55f71f87 |
Download
Original bundle
1 - 1 of 1
