Transport Coefficient

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

The transport coefficients occur in transport phenomenon with transport laws
: $\mathbf_k = \gamma_k \mathbf_k$

where:
: $\mathbf_k$ is a flux of the property $k$
: the transport coefficient $\gamma _k$ of this property $k$
: $\mathbf_k$, the gradient force which acts on the property $k$.

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

:$\gamma = \int_0^\infty \left\langle \dot(t) \dot(0) \right\rangle \, dt,$

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.Water in Biology, Chemistry, and Physics: Experimental Overviews and Computational Methodologies, G. Wilse Robinson, , p. 80
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For times $t$ that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

:$2t\gamma = \left\langle , A(t) - A(0), ^2 \right\rangle.$

In general a transport coefficient is a tensor.

Examples

* Diffusion constant, relates the flux of particles with the negative gradient of the concentration (see Fick's laws of diffusion)
* Thermal conductivity (see Fourier's law)
* Ionic conductivity
* Mass transport coefficient
* Shear viscosity $\eta = \frac \int_0^\infty dt \, \langle \sigma_(0) \sigma_{xy} (t) \rangle$, where $\sigma$ is the viscous stress tensor (see Newtonian fluid)
* Electrical conductivity

See also

*Linear response theory
*Onsager reciprocal relations

References

Thermodynamics
Statistical mechanics