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Statistics of the dissipated energy in driven diffusive systems

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Abstract.

Understanding the physics of non-equilibrium systems remains one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the non-equilibrium behaviour of the system of interest; their statistics, associated structures and microscopic origin. During the last years, some new general and powerful methods have appeared to delve into fluctuating behaviour that have drastically changed the way to address this problem in the realm of diffusive systems: macroscopic fluctuation theory (MFT) and a set of advanced computational techniques that make it possible to measure the probability of rare events. Notwithstanding, a satisfactory theory is still lacking in a particular case of intrinsically non-equilibrium systems, namely those in which energy is not conserved but dissipated continuously in the bulk of the system (e.g. granular media). In this work, we put forward the dissipated energy as a relevant quantity in this case and analyse in a pedagogical way its fluctuations, by making use of a suitable generalisation of macroscopic fluctuation theory to driven dissipative media.

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References

  1. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim, Phys. Rev. Lett. 87, 040601 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  2. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim, Phys. Rev. Lett. 94, 030601 (2005)

    Article  ADS  Google Scholar 

  3. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim, J. Stat. Mech. P07014, (2007)

  4. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim, J. Stat. Phys. 135, 857 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  5. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim, Rev. Mod. Phys. 87, 593 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  6. B. Derrida, J. Stat. Mech. P07023, (2007)

  7. R.S. Ellis, Entropy, Large Deviations and Statistical Mechanics (Springer, New York, 1985)

  8. H. Touchette, Phys. Rep. 478, 1 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  9. T. Pöschel, S. Luding (Editors), Granular Gases, Lecture Notes in Physics, Vol. 564 (Springer-Verlag, Berlin 2001)

  10. A. Prados, A. Lasanta, P.I. Hurtado, Phys. Rev. Lett. 107, 140601 (2011)

    Article  ADS  Google Scholar 

  11. P.I. Hurtado, A. Lasanta, A. Prados, Phys. Rev. E 88, 022110 (2013)

    Article  ADS  Google Scholar 

  12. A. Prados, A. Lasanta, P.I. Hurtado, Phys. Rev. E 86, 031134 (2012)

    Article  ADS  Google Scholar 

  13. C. Kipnis, C. Marchioro, E. Presutti, J. Stat. Phys. 27, 65 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  14. A. Lasanta, A. Manacorda, A. Prados, A. Puglisi, New J. Phys. 17, 083039 (2015)

    Article  ADS  Google Scholar 

  15. C. Lanczos, The Variational Principles of Mechanics (Dover, New York, 1986)

  16. J. Javier Brey, M.J. Ruiz-Montero, F. Moreno, Phys. Rev. E 63, 061305 (2001)

    Article  ADS  Google Scholar 

  17. P. Visco, A. Puglisi, A. Barrat, F. van Wijland, E. Trizac, Eur. Phys. J. B 63, 377 (2006)

    Article  ADS  Google Scholar 

  18. D.R.M. Williams, F.C. MacKintosh, Phys. Rev. E 54, R9 (1996)

    Article  ADS  Google Scholar 

  19. T.P.C. van Noije, M.H. Ernst, Granular Matter 1, 57 (1996)

    Article  Google Scholar 

  20. T.P.C. van Noije, M.H. Ernst, E. Trizac, I. Pagonabarraga, Phys. Rev. E 63, 4326 (1999)

    Article  ADS  Google Scholar 

  21. A. Puglisi, V. Loreto, U. Marini Bettolo Marconi, A. Petri, A. Vulpiani, Phys. Rev. Lett. 81, 3848 (1998)

    Article  ADS  Google Scholar 

  22. M.I. García de Soria, P. Maynar, E. Trizac, Phys. Rev. E 85, 051301 (2012)

    Article  ADS  Google Scholar 

  23. M.I. García de Soria, P. Maynar, E. Trizac, Phys. Rev. E 87, 022201 (2013)

    Article  ADS  Google Scholar 

  24. A. Prados, E. Trizac, Phys. Rev. Lett. 112, 198001 (2013)

    Article  ADS  Google Scholar 

  25. T. Bodineau, B. Derrida, Phys. Rev. Lett. 92, 180601 (2004)

    Article  ADS  Google Scholar 

  26. P.I. Hurtado, P.L. Garrido, Phys. Rev. Lett. 102, 250601 (2009)

    Article  ADS  Google Scholar 

  27. P.I. Hurtado, P.L. Garrido, Phys. Rev. E 81, 041102 (2010)

    Article  ADS  Google Scholar 

  28. P.I. Hurtado, C. Pérez-Espigares, J.J. del Pozo, P.L. Garrido, Proc. Natl. Acad. Sci. U.S.A. 108, 7704 (2011)

    Article  ADS  Google Scholar 

  29. T. Bodineau, B. Derrida, Phys. Rev. E 72, 066110 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  30. P.I. Hurtado, P.L. Garrido, Phys. Rev. Lett. 107, 180601 (2011)

    Article  ADS  Google Scholar 

  31. C.P. Espigares, P.L. Garrido, P.I. Hurtado, Phys. Rev. E 87, 032115 (2013)

    Article  ADS  Google Scholar 

  32. P.I. Hurtado, C. Pérez-Espigares, J.J. del Pozo, P.L. Garrido, J. Stat. Phys. 154, 214 (2014)

    Article  MathSciNet  Google Scholar 

  33. I.M. Gelfand, S.V. Fomin, Calculus of Variations (Dover, New York, 2000)

  34. J.J. Brey, M.J. Ruiz-Montero, F. Moreno, Phys. Rev. E 62, 5339 (2000)

    Article  ADS  Google Scholar 

  35. G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)

    Article  ADS  Google Scholar 

  36. J.L. Lebowitz, H. Spohn, J. Stat. Phys. 95, 333 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  37. A. Puglisi et al., Phys. Rev. Lett. 95, 110202 (2005)

    Article  ADS  Google Scholar 

  38. W.H. Press, S.A. Teukolsky, T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd Edition (Cambridge University Press, New York, 2007)

  39. P. Grassberger, Comp. Phys. Com. 147, 64 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  40. C. Giardinà, J. Kurchan, L. Peliti, Phys. Rev. Lett. 96, 120603 (2006)

    Article  ADS  Google Scholar 

  41. V. Lecomte, J. Tailleur, J. Stat. Mech. P03004, (2007)

  42. V. Lecomte, J. Tailleur, AIP Conf. Proc. 1091, 212 (2009)

    ADS  Google Scholar 

  43. C. Giardin, J. Kurchan, V. Lecomte, J. Tailleur, J. Stat. Phys. 145, 787 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  44. H.J. Harris, G.M. Schütz, J. Stat. Mech. P07020, (2007)

  45. G.M. Schütz, in Phase Transitions and Critical Phenomena, Vol. 19, edited by C. Domb, J.L. Lebowitz (Academic press, London, 2001)

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Authors and Affiliations

  1. CNR-ISC and Dipartimento di Fisica, Università La Sapienza, p.le A. Moro 2, 00185, Rome, Italy

    A. Lasanta

  2. Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071, Granada, Spain

    Pablo I. Hurtado

  3. Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071, Granada, Spain

    Pablo I. Hurtado

  4. Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080, Sevilla, Spain

    A. Prados

Authors
  1. A. Lasanta
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  2. Pablo I. Hurtado
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  3. A. Prados
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Correspondence to A. Lasanta.

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Lasanta, A., Hurtado, P. & Prados, A. Statistics of the dissipated energy in driven diffusive systems. Eur. Phys. J. E 39, 35 (2016). https://doi.org/10.1140/epje/i2016-16035-4

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  • DOI: https://doi.org/10.1140/epje/i2016-16035-4

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