Molecular Simulation/Transport properties

Viscosity
The viscosity of a liquid is defined by the drag force experienced by a moving plate separated from a stationary plate by a layer of the liquid. $$ \tau = \frac{F}{A}= \eta \frac{A \cdot u}{h}$$

u is the speed of the moving plate. h is distance by which the two plates are separated. A is the surface area of the moving plate.

$$\eta$$ can be calculated from a molecular dynamics simulation using the Green–Kubo relation, $$\eta = \frac{V}{k_B T} \int^\infty_0  \langle P_{xy}(t_0) P_{xy} (t_0+\tau) \rangle \textrm{d}\tau$$

Pxy is the xy component of the pressure tensor. The xz or yx off-diagonal components can be used instead.

Thermal Conductivity
The thermal conductivity of a liquid is defined by the rate of heat transfer between an upper and lower plate at different temperatures (T1 and T2).
 * $$ J(J / m^2 / s ) = \lambda \Delta T $$

The Green-Kubo relation for thermal conductivity relates lambda to the autocorrelation function of the heat current,
 * $$ \lambda = \frac{1}{3 V k_B T^2} \int^\infty_0 \langle j(t) \cdot j(t + \tau) \rangle d \tau $$