Hierarchies and Contractions of the Description

Abstract

One of the characteristic features of the mechanistic statistical theory is that it can be used at a variety of levels of description. Indeed, we have seen that molecular processes ranging from momentum and heat transport to electrochemical reactions and molecular scattering events all can be described by the canonical equations in Chapter 4. The amount of molecular detail contained in these descriptions varies tremendously. At the thermodynamic level the extensive variables are characteristic of properties of the entire system, such as the total internal energy. At the hydrodynamic level, on the other hand, one keeps track of densities of extensive variables at each point in space. Finally, at the Boltzmann level the number density of particles in the molecular phase space is the fundamental quantity of interest.