Invited Lecture
The significance and meaning of off-diagonal Onsager phenomenological coefficients

The Onsager phenomenological coefficients of non-equilibrium thermodynamics are often employed in diffusion theory. Indeed, they are generally considered to have been absolutely indispensable in the development of the subject. In this wide ranging lecture we discuss the significance and meaning of the phenomenological coefficients in tracer diffusion, ionic conductivity, interdiffusion and thermotransport. We focus especially on the somewhat enigmatic off-diagonal coefficients. We discuss the Green-Kubo equations that provide an immensely useful way of understanding the physical background of the coefficients and for their calculation by Kinetic Monte Carlo and molecular dynamics. We discuss the relationships of the off-diagonal coefficients to physical diffusion quantities including tracer and collective correlation effects, the vacancy-wind effect and the heat of transport. We draw on examples of diffusion in binary alloys, intermetallics, multicomponent alloys (including high entropy alloys), ionic compounds and diffusion in liquid alloys.