Transport coefficient

measures how rapidly a perturbed system returns to equilibrium.

is an observable occurring in a perturbed Hamiltonian,

is an ensemble average and the dot above the A denotes the time derivative.

that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation: In general a transport coefficient is a tensor.

For strong gradients the transport equation typically has to be modified with higher order terms (and higher order Transport coefficients).