So, I’ve given you a bit of information in these past BMC posts about what statistical mechanics and thermodynamics are all about. These have been all part of the so-called microcanonical ensemble. All of this focuses around examining the individual states of each component of a thermodynamic system (the microstates). The two assumptions of the microcanonical ensemble is that the total number of particles in a system stays fixed, and that the total energy of the system is also fixed. Removing this energy requirement allows us to move into another thermodynamic formulation: the canonical ensemble. This allows us to consider things like a warming bottle of beer as just the bottle of beer, and not the bottle and the environment it is situated in (a much more complicated problem). In order to work within the canonical ensemble, a powerful tool for describing the system is needed. This tool is the Partition Function.