A transport coefficient γ {\displaystyle \gamma } measures how rapidly a perturbed system returns to equilibrium.

The transport coefficients occur in transport phenomenon with transport laws

J k = γ k X k {\displaystyle \mathbf {J} _{k}=\gamma _{k}\mathbf {X} _{k}}

where:

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

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

γ = ∫ 0 ∞ ⟨ A ˙ ( t ) A ˙ ( 0 ) ⟩ d t , {\displaystyle \gamma =\int _{0}^{\infty }\left\langle {\dot {A}}(t){\dot {A}}(0)\right\rangle \,dt,}

where A {\displaystyle A} is an observable occurring in a perturbed Hamiltonian, ⟨ ⋅ ⟩ {\displaystyle \langle \cdot \rangle } is an ensemble average and the dot above the A denotes the time derivative. For times t {\displaystyle t} that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

2 t γ = ⟨ | A ( t ) − A ( 0 ) | 2 ⟩ . {\displaystyle 2t\gamma =\left\langle |A(t)-A(0)|^{2}\right\rangle .}

In general a transport coefficient is a tensor.