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| {{Stub-general}}
| | The Green-Kubo relations can be derived from the [[Evans-Searles transient fluctuation theorem]]. |
| The '''Green-Kubo relations''' <ref>[http://dx.doi.org/10.1063/1.1740082 Melville S. Green "Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids", Journal of Chemical Physics '''22''' pp. 398-413 (1954)]</ref>
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| <ref>[http://dx.doi.org/10.1143/JPSJ.12.570 Ryogo Kubo "Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems", Journal of the Physical Society of Japan '''12''' PP. 570-586 (1957)]</ref>
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| are expressions that relate macroscopic [[transport coefficients]] to integrals of microscopic
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| [[time correlation functions]]. In general one has
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| :<math> L(F_e = 0) =\frac{V}{k_BT} \int_0^\infty \left\langle {J(0)J(s)} \right\rangle _{0} ~{\mathrm{d}} s</math>
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| where <math>L</math> is the linear transport coefficient and <math>J</math> is the flux.
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| ==Shear viscosity==
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| The [[Viscosity |shear viscosity]] is related to the [[Pressure |pressure tensor]] via
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| :<math>\eta = \frac{V}{k_BT}\int_0^{\infty} \langle p_{xy}(0) p_{xy}(t) \rangle ~{\mathrm{d}} t</math>
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| i.e. the integral of the autocorrelation of the off-diagonal components of the microscopic [[Stress| stress tensor]].
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| ==Fluctuation theorem==
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| The Green-Kubo relations can be derived from the [[Evans-Searles transient fluctuation theorem]]<ref>[http://dx.doi.org/10.1063/1.481610 Debra J. Searles and Denis J. Evans "The fluctuation theorem and Green–Kubo relations", Journal of Chemical Physics '''112''' pp. 9727-9735 (2000)]</ref> | |
| ==References== | | ==References== |
| <references/>
| | #[http://dx.doi.org/10.1063/1.481610 Debra J. Searles and Denis J. Evans "The fluctuation theorem and Green–Kubo relations", Journal of Chemical Physics '''112''' pp. 9727-9735 (2000)] |
| '''Related reading'''
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| *Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press, 3rd Edition (2006) ISBN 0-12-370535-5 ([http://dx.doi.org/10.1016/B978-012370535-8/50009-4 chapter 7])
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| * Denis J. Evans and Gary Morriss "Statistical Mechanics of Nonequilibrium Liquids", Cambridge University Press, 2nd Edition (2008) ISBN 9780521857918 (Chapter 4)
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| [[Category: Non-equilibrium thermodynamics]] | | [[Category: Non-equilibrium thermodynamics]] |