Green-Kubo relationship

Equilibrium molecular dynamics uses the Green-Kubo relationship between the heat current autocorrelation function and the thermal conductivity [66] to obtain the thermal conductivity as ... 

Equations (18.69) and (18.70) are examples of Green-Kubo relationships [7, 81 between an equilibrium correlation function and a transport coefficient, the diffusion constant D in this case. There are several such relationships. Without going into the details, we just note that another such relationship gives the friction coefficient in terms of the force correlation function ... 

In addition, the viscosity is the autocorrelation function of momentum transfer in liquid flow s. Green-Kubo relationships equate a kinetic property (such as the diffusion coefficient or the friction coefficient) with an ensemble average of an equilibrium property, such as (v(O)v(t)). 

The thermal conductivity of a material can be calculated directly from equilibrium molecular dynamics (EMD) simulation based on the linear response theory Green-Kubo relationship. " The fluctuation-dissipation theorem provides a connection between the energy dissipation in irreversible processes and the thermal fluctuations in equilibrium. The thermal conductivity tensor. A, can be expressed in terms of heat current autocorrelation correlation functions (HCACFs),/, ... 

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