Europhys. Lett.
Volume 73, Number 2, January 2006
Page(s) 183 - 189
Section General
Published online 14 December 2005
Europhys. Lett., 73 (2), pp. 183-189 (2006)
DOI: 10.1209/epl/i2005-10384-7

New Green-Kubo formulas for transport coefficients in hard-sphere, Langevin fluids and the likes

M. H. Ernst1, 2 and R. Brito2

1  Institute for Theoretical Physics, Universiteit Utrecht 3508 TD Utrecht, The Netherlands
2  Departamento de Física Aplicada I and GISC, Universidad Complutense 28040 Madrid, Spain

received 21 August 2005; accepted in final form 22 November 2005
published online 14 December 2005

We present generalized Green-Kubo expressions for thermal transport coefficients $\mu$ in non-conservative fluid-type systems, of the generic form $\mu = \mu_\infty +\int^\infty_0
\upd t V^{-1} \langle{I_\epsilon \exp[t {\cal L}] I}\rangle_0$, where $\exp[t{\cal
L}]$ is a pseudo-streaming operator. It consists of a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current I and its conjugate current $I_\epsilon$. This formula with $\mu_\infty \neq 0$ and $I_\epsilon \neq I$ covers vastly different systems, such as strongly repulsive elastic interactions in hard-sphere fluids, weakly interacting Langevin fluids with dissipative and stochastic interactions satisfying detailed balance conditions, and "the likes", defined in the text. For conservative systems the results reduce to the standard formulas.

05.40.-a - Fluctuation phenomena, random processes, noise and Brownian motion.
05.20.Dd - Kinetic theory.

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