Journal of Low Temperature Physics

, Volume 185, Issue 1–2, pp 79–86 | Cite as

Gauge Invariance of Thermal Transport Coefficients

  • Loris Ercole
  • Aris Marcolongo
  • Paolo Umari
  • Stefano Baroni


Thermal transport coefficients are independent of the specific microscopic expression for the energy density and current from which they can be derived through the Green–Kubo formula. We discuss this independence in terms of a kind of gauge invariance resulting from energy conservation and extensivity, and demonstrate it numerically for a Lennard-Jones fluid, where different forms of the microscopic energy density lead to different time correlation functions for the heat flux, all of them, however, resulting in the same value for the thermal conductivity.


Thermal conductivity Heat transport Hydrodynamic fluctuations Molecular dynamics Green–Kubo 


  1. 1.
    M.S. Green, J. Chem. Phys. 22, 398 (1954)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)ADSCrossRefGoogle Scholar
  3. 3.
    L.P. Kadanoff, P.C. Martin, Ann. Phys. 24, 419 (1963)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, Reading, 1975)Google Scholar
  5. 5.
    A. Marcolongo, P. Umari, S. Baroni, Nat. Phys. 12, 80–84 (2015). doi: 10.1038/nphys3509 CrossRefGoogle Scholar
  6. 6.
    J.-P. Hansen, I.R. McDonald, Theory of Simple Liquids, 3rd edn. (Elsevier, Philadelphia, 2006)MATHGoogle Scholar
  7. 7.
    Y. Lee, R. Biswas, C. Soukoulis, C. Wang, C. Chan, K.M. Ho, Phys. Rev. B 43, 6573 (1991)ADSCrossRefGoogle Scholar
  8. 8.
    A. Marcolongo, SISSA Ph.D. Thesis,
  9. 9.
    S. Plimpton, CMD simulations have been performed using the LAMMPS code, J. Comp. Phys. 117, 1 (1995),
  10. 10.
    R. Resta, D. Vanderbilt, Top. Appl. Phys. 105, 31 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Loris Ercole
    • 1
  • Aris Marcolongo
    • 2
  • Paolo Umari
    • 3
  • Stefano Baroni
    • 1
  1. 1.SISSA – Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Dipartimento di Fisica ed AstronomiaUniversità di PadovaPadovaItaly

Personalised recommendations