Advertisement

Temperature and correlations in 1-dimensional systems

  • Claudio Giberti
  • Lamberto Rondoni
  • Cecilia VerniaEmail author
Regular Article
  • 13 Downloads
Part of the following topical collections:
  1. Microscopic Dynamics, Chaos and Transport in Nonequilibrium Processes

Abstract

Local thermodynamic equilibrium (LTE) plays a crucial role in statistical mechanics and thermodynamics. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the systems at hand are represented by the transport coefficients. The robustness and universality of equilibrium properties is not guaranteed in nonequilibrium states, in which different microscopic quantities may behave differently, even if they coincide at equilibrium. We investigate these issues considering 1-dimensional chains of N oscillators. We observe that non-negligible fluctuations, and persistence of correlations frustrate the onset of LTE, hence the existence of thermodynamic fields, such as temperature.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Z. Rieder Z, J.L. Lebowitz, E. Lieb, J. Math. Phys. 8, 1073 (1967) ADSCrossRefGoogle Scholar
  2. 2.
    M. Colangeli, C. Giardinà , C. Giberti, C. Vernia, Phys. Rev. E 97, 030103(R) (2018) ADSCrossRefGoogle Scholar
  3. 3.
    L.D. Landau, E.M. Lifshitz, in Statistical Physics (Pergamon Press, Oxford, 1980), Vol. 5 Google Scholar
  4. 4.
    S. Chibbaro, L. Rondoni, A. Vulpiani, Reductionism, Emergence and Levels of Reality (Springer Verlag, New York, 2014) Google Scholar
  5. 5.
    D. Kondepudi, I. Prigogine, Modern thermodynamics: from heat engines to dissipative structures (John Wiley & Sons Ltd., Chichester, 1998) Google Scholar
  6. 6.
    H. Spohn, Large Scale Dynamics of Interacting Particles, Texts and Monographs in Physics (Springer-Verlag, Heidelberg, 1991) Google Scholar
  7. 7.
    J. Bellissard, in Dynamics of Dissipation, edited by P. Garbaczewski, R. Olkiewicz (Springer Verlag, Berlin, 2002) Google Scholar
  8. 8.
    H.J. Kreuzer, Nonequilibrium thermodynamics and its statistical foundations (Clarendon Press, Oxford, 1981) Google Scholar
  9. 9.
    M. Falcioni, L. Palatella, S. Pigolotti, L. Rondoni, A. Vulpiani, Physica A 385, 170 (2007) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    L. Rondoni, S. Pigolotti, Phys. Scr. 86, 058513 (2012) CrossRefGoogle Scholar
  11. 11.
    M. Bonaldi et al., Phys. Rev. Lett. 103, 010601 (2009) ADSCrossRefGoogle Scholar
  12. 12.
    L. Conti, M. Bonaldi, L. Rondoni, Quant. Grav. 27, 084032 (2010) ADSCrossRefGoogle Scholar
  13. 13.
    C.W. Chang, D. Okawa, H. Garcia, A. Majumdar, A. Zettl, Phys. Rev. Lett. 101, 075903 (2008) ADSCrossRefGoogle Scholar
  14. 14.
    X. Xu et al., Nat. Commun. 5, 3689 (2014) CrossRefGoogle Scholar
  15. 15.
    O.G. Jepps, L. Rondoni, J. Phys. A 39, 1311 (2006) ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    C. Giberti, L. Rondoni, Phys. Rev. E 83, 041115 (2011) ADSCrossRefGoogle Scholar
  17. 17.
    S. Chen, Y. Zhang, J. Wang, H. Zhao, J. Stat. Mech. 2016, 033205 (2016) CrossRefGoogle Scholar
  18. 18.
    S. Chen, Y. Zhang, J. Wang, H. Zhao, Phys. Rev. E 87, 032153 (2013) ADSCrossRefGoogle Scholar
  19. 19.
    M. Onorato, L. Vozella, D. Proment, Y.V. Lvov, Proc. Natl. Acad. Sci. USA 112, 4208 (2015) ADSCrossRefGoogle Scholar
  20. 20.
    A. Dhar, K. Saito, Phys. Rev. E 78, 061136 (2008) ADSCrossRefGoogle Scholar
  21. 21.
    G.P. Morriss, L. Rondoni, Phys. Rev. E 59, R5 (1999) ADSCrossRefGoogle Scholar
  22. 22.
    J. Casas-Vázquez, D. Jou, Rep. Prog. Phys. 66, 2003 1937 Google Scholar
  23. 23.
    D. Jou, L. Restuccia, Physica A 460, 246 (2016) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    D.J. Jou, J. Casas-Vàzquez, G. Lebon, Extended Irreversible Thermodynamics (Springer, New York, 2010) Google Scholar
  25. 25.
    M. Criado-Sancho, D. Jou, J. Casas-Vázquez, Phys. Lett. A 350, 339 (2006) ADSCrossRefGoogle Scholar
  26. 26.
    X. Cao, D. He, Phys. Rev. E 92, 032135 (2015) ADSCrossRefGoogle Scholar
  27. 27.
    A. Puglisi, A. Sarracino, A. Vulpiani, Phys. Rep. 709–710, 1 (2017) CrossRefGoogle Scholar
  28. 28.
    K. Huang, Statistical Mechanics (John Wiley & Sons, New York, 1963) Google Scholar
  29. 29.
    G. Gallavotti, Statistical Mechanics (Springer, New York, 1999) Google Scholar
  30. 30.
    H.H. Rugh, Phys. Rev. Lett. 78, 772 (1997) ADSCrossRefGoogle Scholar
  31. 31.
    O.G. Jepps, L. Rondoni, J. Phys. A 43, 133001 (2010) ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    L. Conti et al., J. Stat. Mech. 2013, P12003 (2013) CrossRefGoogle Scholar
  33. 33.
    J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006) Google Scholar
  34. 34.
    G. Gallavotti, Nonequilibrium and Irreversibility (Springer, New York, 2014) Google Scholar
  35. 35.
    D.J. Evans, S.R. Williams, D.J. Searles, L. Rondoni, J. Stat. Phys. 164, 842 (2016) ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    M.W. Zemansky, R.H. Dittman, Heat and Thermodynamics (McGraw-Hill, New York, 1997) Google Scholar
  37. 37.
    S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics (Dover, New York, 1984) Google Scholar
  38. 38.
    O. Narayan, S. Ramaswamy, Phys. Rev. Lett. 89, 200601 (2002) ADSCrossRefGoogle Scholar
  39. 39.
    T. Mai, O. Narayan, Phys. Rev. E 73, 061202 (2006) ADSCrossRefGoogle Scholar
  40. 40.
    L. Delfini, S. Lepri, R. Livi, A. Politi, Phys. Rev. E 73, 060201(R) (2006) ADSCrossRefGoogle Scholar
  41. 41.
    S. Lepri, C. Mejía-Monasterio, A. Politi, J. Phys. A 43, 065002 (2010) ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    L. Delfini, S. Lepri, R. Livi, C. Mejía-Monasterio, A. Politi, J. Phys. A 43, 145001 (2010) ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    C. Giberti, L. Rondoni, C. Vernia, https://doi.org/arXiv:1706.02886 [cond-mat.stat-mech] (2018)
  44. 44.
    P. De Gregorio, L. Rondoni, M. Bonaldi, L. Conti, Phys. Rev. B 84, 224103 (2011) ADSCrossRefGoogle Scholar
  45. 45.
    L. Conti, P. De Gregorio, M. Bonaldi, A. Borrielli, M. Crivellari, G. Karapetyan, C. Poli, E. Serra, R.K. Thakur, L. Rondoni, Phys. Rev. E 85, 066605 (2012) ADSCrossRefGoogle Scholar
  46. 46.
    G. Falasco, F. Baldovin, K. Kroy, M. Baiesi, New J. Phys. 18, 093043 (2016) ADSCrossRefGoogle Scholar
  47. 47.
    S. Lepri, R. Livi, A. Politi, Phys. Rep. 377, 1 (2003) ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    S. Lepri, R. Livi, A. Politi, Phys. Rev. Lett. 78, 1896 (1997) ADSCrossRefGoogle Scholar
  49. 49.
    S. Lepri, R. Livi, A. Politi, Physica D 119, 140 (1998) ADSCrossRefGoogle Scholar
  50. 50.
    A. Dhar, Adv. Phys 57, 457 (2008) ADSCrossRefGoogle Scholar
  51. 51.
    S. Lepri, in Thermal transport in low dimensions – From Statistical Physics to Nanoscale Heat Transfer, Lecture Notes in Physics (Springer, Heidelberg, 2016), Vol. 921 Google Scholar
  52. 52.
    P.I. Hurtado, Phys. Rev. Lett. 96, 010601 (2006) ADSCrossRefGoogle Scholar
  53. 53.
    S.J. Davie, O.G. Jepps, L. Rondoni, J.C. Reid, D.J. Searles, Phys. Scr. 89, 048002 (2014) ADSCrossRefGoogle Scholar
  54. 54.
    O. Jepps, C. Bianca, L. Rondoni, Chaos 18, 013127 (2008) ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    C. Bianca, L. Rondoni, Chaos 19, 013121 (2009) ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    L. Salari, L. Rondoni, C. Giberti, R. Klages, Chaos 25, 073113 (2015) ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    A.I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover Publications, New York, 1949) Google Scholar
  58. 58.
    S. Chibbaro, L. Rondoni, A. Vulpiani, Commun. Theor. Phys. 62, 469 (2014) CrossRefGoogle Scholar
  59. 59.
    D. Alonso, R. Artuso, G. Casati, I. Guarneri, Phys. Rev. Lett. 82, 1859 (1999) ADSCrossRefGoogle Scholar
  60. 60.
    B. Li, L. Wang, B. Hu, Phys. Rev. Lett. 88, 223901 (2002) ADSCrossRefGoogle Scholar
  61. 61.
    M. Colangeli, L. Rondoni, J. Stat. Mech. Theor. Exp. 2013, P02009 (2013) CrossRefGoogle Scholar
  62. 62.
    M. Colangeli, M. Pizzi, L. Rondoni, Physica A 392, 2977 (2013) ADSMathSciNetCrossRefGoogle Scholar
  63. 63.
    T. Vanzan, L. Rondoni, Physica A 493, 370 (2018) ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Claudio Giberti
    • 1
  • Lamberto Rondoni
    • 2
  • Cecilia Vernia
    • 3
    Email author
  1. 1.Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio EmiliaReggio EmiliaItaly
  2. 2.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  3. 3.Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio EmiliaModenaItaly

Personalised recommendations