A Transport coefficient \gamma 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.[1] For times t that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

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


Diffusion constant, relates the flux of particles with the negative gradient of the concentration (see Fick's laws of diffusion)
Heat transport coefficient
Mass transport coefficient
Shear Viscosity \eta = \frac{1}{k_BT V}\int_0 ^\infty dt \langle \sigma(0)_{xy} \sigma_{xy} (t) \rangle
Electrical conductivity

See also

Linear response theory


Water in Biology, Chemistry, and Physics: Experimental Overviews and Computational Methodologies, G. Wilse Robinson, ISBN 9789810224516, p. 80, Google Books

Physics Encyclopedia

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