Simple Systems without Interactions

Abstract

In this chapter we present some applications of ST to very simple systems. The simplicity here arises from either negligible or total absence of interparticle interactions. Lack of interaction usually implies independence of the particles. This, in turn, leads to a relatively easy solution for the PF of the system. A total lack of interactions never exists in real systems. Nevertheless, such idealized systems are interesting for two reasons. First, some systems behave, to a good approximation, as if there are no interactions (e.g., a real gas at very low densities, adsorption of molecules on sites that are far apart). Second, real systems with interactions can be viewed and treated as extensions of idealized simple systems. For instance, the theory of real gases is based on corrections due to interactions between pairs, triplets, etc. Even in the very simple systems, some interactions between particles or between particles and an external field are essential to the maintenance of equilibrium. Lack of interactions usually leads to solvability of the PF, but this is not always so. In Chapter 3 we shall study systems with interactions among a small number of particles for which a PF can be written explicitly. Likewise, the inherent simplicity of the one-dimensional systems studied in Chapter 4 also leads to solvability of the PF.