Statistical Mechanics from a Quantum Perspective
An energy level consists of all microscopic states of a system with the same energy. The energy levels of a system depend on the number of particles and the volume. At each instance in time, many different quantum states are represented in the various systems in the ensemble. A microcanonical ensemble describes an isolated system which has a fixed energy, volume and number of particles. The chapter describes certain relationships between fluctuations in thermodynamical variables and some other thermodynamical entities. One case of particular interest is when each subsystem is composed of one single particle, for instance very weakly interacting particles adsorbed on a surface or the particles in an ideal gas. The chapter presents more strict derivations of the probability expressions in the canonical, isobaric-isothermal and grand canonical ensembles. Volume and number of particles can also be considered as being mechanical variables. Entropy and temperature are examples of nonmechanical variables.