The Bicomponent Ensemble

The simplest cluster ensemble is formed by partitioning an extensive variable M, which we have called “mass,” into N clusters. In Chap. 3 we generalized this to the partitioning of a set of extensive variables, X ₁ , X ₂ , ⋯ into N clusters. X _i may represent energy, volume, or any other extensive attribute that is distributed. A special case is when this attribute refers to a distinct species that we recognize as a component. A population that contains two or more components forms a mixture and its behavior is quite different from that of the generic multivariate ensemble. All extensive properties of a multicomponent population may be sub-partitioned with respect to components. In this chapter we formulate the bicomponent cluster ensemble, derive its thermodynamics, and study the mixing of components for certain classes of selection functionals.