Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation

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

Volumn 88, Issue 2, 2013, Pages

  Hurtado, Pablo I ^a   Lasanta, A ^b   Prados, A ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CENTRAL LIMIT THEOREM; DISSIPATIVE SYSTEMS; DRIVEN DIFFUSIVE SYSTEMS; EULER-LAGRANGE EQUATIONS; GALLAVOTTI-COHEN FLUCTUATION; HYDRODYNAMIC EQUATIONS; MICROSCOPIC DYNAMICS; NONLINEAR DIFFUSION;

ENERGY DISSIPATION; EQUATIONS OF MOTION; PHASE SPACE METHODS; PROBABILITY DISTRIBUTIONS;

SUPERCONDUCTING MATERIALS;

EID: 84883860389     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.022110     Document Type: Article

References (53)

1. A. Einstein, Investigation on the Theory of Brownian Movement, edited by, R. Fürth, (Dover, New York, 1956).
2. H. B. Callen and T. A. Welton, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.83.34 83, 34 (1951).
3. R. Kubo, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/29/1/306 29, 255 (1966).
4. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Course of Theoretical Physics, Vol. 5 (Pergamon Press, Oxford, 1980).
5. R. S. Ellis, Entropy, Large Deviations and Statistical Mechanics (Springer, New York, 1985).
6. H. Touchette, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2009.05.002 478, 1 (2009).
7. G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.2694 74, 2694 (1995).
8. J. L. Lebowitz and H. Spohn, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1004589714161 95, 333 (1999).
9. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.040601 87, 040601 (2001);
10. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.030601 94, 030601 (2005); (Pubitemid 40607273)
11. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, J. Stat. Mech. 10.1088/1742-5468/2007/07/P07014 (2007) P07014;
12. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-008-9670-4 135, 857 (2009).
13. B. Derrida, J. Stat. Mech. 1742-5468 10.1088/1742-5468/2007/07/P07023 (2007) P07023.
14. T. Bodineau and B. Derrida, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.180601 92, 180601 (2004).
15. P. I. Hurtado and P. L. Garrido, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.250601 102, 250601 (2009);
16. P. I. Hurtado and P. L. Garrido, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.041102 81, 041102 (2010).
17. C. Pérez-Espigares, J. J. del Pozo, P. L. Garrido, and P. I. Hurtado, AIP Conf. Proc. APCPCS 0094-243X 10.1063/1.3569502 1332, 204 (2011).
18. P. I. Hurtado and P. L. Garrido, J. Stat. Mech. 10.1088/1742-5468/2009/ 02/P02032 (2009) P02032.
19. P. I. Hurtado, C. Pérez-Espigares, J. J. del Pozo and P. L. Garrido, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.1013209108 108, 7704 (2011).
20. J. J. Brey, M. I. García de Soria, P. Maynar, and M. J. Ruiz-Montero, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.098001 94, 098001 (2005). (Pubitemid 40620633)
21. J. Murray, Mathematical Biology (Springer-Verlag, Berlin, 2002).
22. S. T. Bramwell, P. C. W. Holdsworth, and J.-F. Pinton, Nature (London) NATUAS 0028-0836 10.1038/25083 396, 552 (1998). (Pubitemid 28563710)
23. S. Ramaswamy, Annu. Rev. Condens. Matter Phys. 1947-5454 10.1146/annurev-conmatphys-070909-104101 1, 323 (2010);
24. M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. Aditi Simha, Rev. Mod. Phys. 10.1103/RevModPhys.85.1143 85, 1143 (2013).
25. I. Epstein and J. Pojman, An Introduction to Nonlinear Chemical Dynamics (Oxford University Press, Oxford, 1998);
26. A. De Wit, Adv. Chem. Phys. 9780-4701 10.1002/9780470141687.ch5 109, 435 (1999);
27. P. Gaspard, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1688758 120, 8898 (2004).
28. R. S. Cantrell and C. Corner, Spatial Ecology via Reaction-Diffusion Equations (Wiley, New York, 2003).
29. A. Prados, A. Lasanta, and P. I. Hurtado, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.140601 107, 140601 (2011).
30. A. Prados, A. Lasanta, and P. I. Hurtado, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.031134 86, 031134 (2012).
31. C. Kipnis, C. Marchioro, and E. Presutti, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01011740 27, 65 (1982).
32. C. Giardinà, J. Kurchan, and L. Peliti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.120603 96, 120603 (2006).
33. T. Bodineau and M. Lagouge, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-010-9934-7 139, 201 (2010).
34. G. Jona-Lasinio, C. Landim, and M. E. Vares, Probab. Theory Relat. Fields PTRFEU 0178-8051 10.1007/BF01195070 97, 339 (1993).
35. T. Bodineau and B. Derrida, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.72.066110 72, 066110 (2005). (Pubitemid 43273018)
36. P. I. Hurtado and P. L. Garrido, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.180601 107, 180601 (2011).
37. Carlos P. Espigares, Pedro L. Garrido, and P. I. Hurtado, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.032115 87, 032115 (2013).
38. I. M. Gelfand and S. V. Fomin, Calculus of Variations (Dover, New York, 2000).
39. C. Lanczos, The Variational Principles of Mechanics (Dover, New York, 1986).
40. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (New York, Springer, 1999).
41. 0 at all these extrema. The possibility of an infinite (continuum) set of extrema is ruled out because of the smoothness of Q (y) for the typical systems of interest.
42. J. P. Boon, J. F. Lutsko, and C. Lutsko, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.021126 85, 021126 (2012).
43. - t, with the property Γ (z + 1) = z Γ (z).
44. P. I. Hurtado and P. L. Krapivsky, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.060103 85, 060103 (R) (2012).
45. T. Pöschel and S. Luding (eds.), Granular Gases, Lecture Notes in Physics, Vol. 564 (Springer-Verlag, Berlin, 2001).
46. In the simulations, time is measured in Monte Carlo steps. A Monte Carlo step comprises N collision events of the microscopic dynamics introduced in Sec.. On the other hand, the unit of our continuous time scale t comprises N 2 Monte Carlo steps.
47. V. Lecomte and J. Tailleur, J. Stat. Mech. 10.1088/1742-5468/2007/03/ P03004 (2007) P03004;
48. J. Tailleur and V. Lecomte, AIP Conf. Proc. 10.1063/1.3082284 1091, 212 (2009).
49. C. Giardina, J. Kurchan, V. Lecomte, and J. Tailleur, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-011-0350-4 145, 787 (2011).
50. The parameter s appearing in the Legendre transform of G (d) is conjugated to the dissipation via the equation s = - ∂ G / ∂ d and turns out to be just minus the Lagrange multiplier λ introduced in Appendix for the constrained variational problem, s = - λ.
51. A. Puglisi, P. Visco, A. Barrat, E. Trizac, and F. van Wijland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.110202 95, 110202 (2005). (Pubitemid 41505735)
52. j = 0 also corresponded to the average behavior.
53. P. L. Krapivsky and B. Meerson, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.031106 86, 031106 (2012).