Maximal Entropy Principles
In this chapter we examine the surprising consequences of maximizing the Boltzmann-Gibbs entropy subject to various constraints. In Section A we show that for a system operating in a phase space of finite measure with no other constraints, the entropy will assume a maximal value if and only if the density (in the terminology of Gibbs) is the density of the microcanonical ensemble. Further, in Section B for a general phase space it is demonstrated that given the expectation value of a particular observable, the Boltzmann-Gibbs entropy of a density will attain its maximum if and only if the density is a generalization of the density of the canonical ensemble.
Unable to display preview. Download preview PDF.