Publication: Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic, and conservative interactions
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2005-12
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American Physical Society
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Abstract
We present a generalization of the Green-Kubo expressions for thermal transport coefficients mu in complex fluids of the generic form mu=mu(infinity)+integral(infinity)(0) dtV(-1)< J(epsilon)exp(tL)J >(0), i.e. a sum of an instantaneous transport coefficient mu(infinity), and a time integral over a time correlation function in a state of thermal equilibrium between a current J and its conjugate current J(epsilon). The streaming operator exp(tL) generates the trajectory of a dynamical variable J(t)=exp(tL)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(infinity)not equal 0 and J(epsilon)not equal 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.
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©2005 The American Physical Society. M.H.E. is supported by SecretarÃa de Estado de Educación y Universidades (Spain), and R.B. by the Universidad Complutense (Profesores en el Extranjero). This work is financed by the research project FIS2004-271 (Spain).
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