Green-Kubo relations

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The Green-Kubo relations [1] [2] are expressions that relate macroscopic transport coefficients to integrals of microscopic time correlation functions. In general one has

where is the linear transport coefficient and is the flux.

Shear viscosity[edit]

The shear viscosity is related to the pressure tensor via

i.e. the integral of the autocorrelation of the off-diagonal components of the microscopic stress tensor.

Fluctuation theorem[edit]

The Green-Kubo relations can be derived from the Evans-Searles transient fluctuation theorem[3]


Related reading

  • Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press, 3rd Edition (2006) ISBN 0-12-370535-5 (chapter 7)
  • Denis J. Evans and Gary Morriss "Statistical Mechanics of Nonequilibrium Liquids", Cambridge University Press, 2nd Edition (2008) ISBN 9780521857918 (Chapter 4)