Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic and conservative interactions

Abstract

We present a generalization of the Green-Kubo expressions for thermal transport coefficients $\mu$ in complex fluids of the generic form, $\mu ={\mu }_{\infty }+{\int }_0^{\infty }dt{V}^{-1}<J_{\epsilon }\exp (t\mathcal{L})J{>}_0$, i.e. 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 $J$ and a transformed current $J_{\epsilon }$. The streaming operator $\exp (t\mathcal{L})$ generates the trajectory of a dynamical variable $J(t)=\exp (t\mathcal{L})J$ when used inside the thermal average $<...{>}_0$. These formulas are valid for conservative, impulsive (hard spheres), stochastic and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general ${\mu }_{\infty }\ne 0$ and $J_{\epsilon }\ne J$, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid.

14 pages, no figures. Version 2: expanded Introduction and section II specifying the classes of fluids covered by this theory. Some references added and typos corrected

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Cited by in corpus (3)

• Theory of Transport Processes and the Method of the Nonequilibrium Statistical Operator
• Nonequilibrium Green-Kubo relations for hydrodynamic transport from an equilibrium-like fluctuation-response equality
• New Green-Kubo formulas for transport coefficients in hard sphere-, Langevin fluids and the likes