TABLE OF CONTENTS Consider a physical system in equilibrium (both internally and with its surroundings) that can exchange only energy with its environment. The corresponding ensemble is then canonical, and each of its members can exist in one of the quantum states characteristic of the isolated system.
Let the number of systems that are in the jth quantum state be n j. Then the set of number { n j} defines the state of the ensemble, and the possible sets { n j} must be considered. That is, we need to determine which { n j} are legitimate possible states of the ensemble. But the only restrictions on the ensemble are the values of the macroscopic parameters in its definition. For the canonical ensemble, the energies of the member systems may differ from one another, but they must always add up to the total energy of the ensemble, which is a constant. There are clearly many sets { n j} that are consistent with a total constant energy of the ensemble, and there is a large number of quantum states for a given set. A particular set { n j} will be called a state distribution of the ensemble, while a particular quantum state of the ensemble will be called a complexion. An ensemble can have many state distributions, and each distribution can have many complexions.
Number the ensemble members from 1 to X and consider a given state...
