Lecture 3 -- Ensembles: the fundamental principles
of statistical mechanics
In the previous Lecture, the rationale for averaging measurements on molecular systems was discussed. Operational averages of experimental data, either time averages or ensemble averages, can be made in a straightforward manner. The computations required for the theoretical analog of an operational time average are extremely cumbersome, and require data -- almost certainly unavailable -- on initial conditions. Lecture 2 concluded by suggesting that an alternative way to develop the theory would be to replace the operational average with an idealized average.
This Lecture develops the basic principles that dominate the remainder of the course. The basic concepts of the ensemble and the ensemble average are introduced. A convenient image for representing ensemble averages is presented. The fundamental properties of the canonical ensemble, and of other less important ensembles, are developed. Finally, useful notation for representing the Hamiltonian coordinates of many-particle systems is given.