In this chapter we take up the problems outlined at the end of the last chapter: How are we to justify the fundamental assumptions needed for non-equilibrium statistical mechanics? How are we to show their consistency with the underlying dynamics? Although most of the important answers to these questions are covered in this chapter, one approach, the approach that invokes cosmological features of the universe “in the large,” is reserved for Chapter 8.

Because the organizational structure of this long chapter is a bit complex, it might be useful to outline here the route we shall follow through the issues. Part I deals with two important preliminaries from experimental science and from the use of computers to model the evolution of dynamical systems. These are results that later will be referred to a number of times in different contexts. Part II outlines the programs that have been offered to “back up” the three approaches to the derivation of a kinetic equation we examined in Chapter 6. Part III then takes up the various basic approaches that have been suggested to provide a physical explanatory context for the success of statistical mechanics in the non-equilibrium situation. First, a number of “unorthodox” approaches are discussed.