Transport coefficient

A Transport coefficient ${\displaystyle \gamma }$ can be expressed via a Green-Kubo relation:

where ${\displaystyle A}$ is an observable occurring in a perturbed Hamiltonian, ${\displaystyle \langle \cdot \rangle }$ is an ensemble average and the dot above the A denotes the time derivative. For times ${\displaystyle t}$ that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

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