Green-Kubo relations

The Green–Kubo relations (Melville S. Green 1954, Ryogo Kubo 1957) give the exact mathematical expression for transport coefficients ${\displaystyle \gamma }$ in terms of integrals of time correlation functions:

Thermodynamic systems may be prevented from relaxing to equilibrium because of the application of a mechanical field (e.g. electric or magnetic field), or because the boundaries of the system are in relative motion (shear) or maintained at different temperatures, etc. This generates two classes of nonequilibrium system: mechanical nonequilibrium systems and thermal nonequilibrium systems.

The standard example of an electrical transport process is Ohm's law, which states that, at least for sufficiently small applied voltages, the current I is linearly proportional to the applied voltage V,

As the applied voltage increases one expects to see deviations from linear behavior. The coefficient of proportionality is the electrical conductance which is the reciprocal of the electrical resistance.

The standard example of a mechanical transport process is Newton's Law of viscosity, which states that the shear stress ${\displaystyle S_{xy}}$ is linearly proportional to the strain rate. The strain rate ${\displaystyle \gamma }$ is the rate of change streaming velocity in the x-direction, with respect to the y-coordinate, ${\displaystyle \gamma \ {\stackrel {\mathrm {def} }{=}}\ \partial u_{x}/\partial y}$. Newton's Law of viscosity states

...
Wikipedia