Transport coefficient

A transport coefficient is a proportionality constant that quantifies how rapidly a physical system responds to a gradient — of temperature, velocity, concentration, or electric potential — by transporting the corresponding quantity (heat, momentum, mass, or charge). It is the macroscopic fingerprint of microscopic dynamics: viscosity measures momentum transport, thermal conductivity measures heat transport, and diffusion coefficients measure mass transport.

The central achievement of modern statistical mechanics has been to show that transport coefficients are not independent empirical constants but are computable from microscopic physics. The Green-Kubo relations express them as integrals of equilibrium correlation functions, and the Kubo formula derives them from linear response theory. This places transport coefficients at the intersection of phenomenology and first-principles physics: they are the numbers that engineers measure and that theorists compute.

From a systems perspective, a transport coefficient is the relaxation rate of a macroscopic mode. It measures how quickly a local perturbation dissipates into the surrounding medium, and it is determined by the same microscopic collisions and correlations that produce equilibrium fluctuations. The transport coefficient is not merely a material property; it is the signature of how a system forgets.