Discovered by: Lars Onsager, awarded the 1968 Nobel Prize in Chemistry.
What is it? Sometimes called the Fourth Law of Thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists.
Why is it important? For many kinetic systems, like the Boltzmann equation or chemical kinetics, the Onsager relations are closely connected to the principle of detailed balance and follow from them in the linear approximation near equilibrium.