Transport coefficients

A transport coefficient $\gamma$ measures how rapidly a perturbed system returns to equilibrium.

The transport coefficients occur in transport phenomenon with transport laws ${\mathbf{J} {_k}} \, = \, \gamma_k \, \mathbf{X} {_k}$ where:

${\mathbf{J}{_k}}$ is a flux of the property $k$
the transport coefficient $\gamma _k$ of this property $k$
${\mathbf{X}{_k}}$, the gradient force which acts on the property $k$.

Transport coefficients can be expressed via a Green–Kubo relation:

$\gamma= \int_0^\infty \langle \dot{A}(t) \dot{A}(0) \rangle \, dt,$

where $A$ is an observable occurring in a perturbed Hamiltonian, $\langle \cdot \rangle$ is an ensemble average and the dot above the A denotes the time derivative.<ref>Water in Biology, Chemistry, and Physics: Experimental Overviews and Computational Methodologies, G. Wilse Robinson, Template:ISBN, p. 80, Google Books</ref> For times $t$ that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

$2t\gamma=\langle |A(t)-A(0)|^2 \rangle.$

In general a transport coefficient is a tensor.

Transport coefficients, like shear viscosity and bulk viscosity, are important for the description of fireball expansion in heavy-ion collisions.