ABSTRACT
In this chapter, the reader see that a similar probabilistic reasoning applies to the group itself. Indeed, every property, be it individual or collective, can be accessed by performing averages. Gibbs proposes calculating the average of microscopic mechanical properties for every state consistent with the few parameters necessary to define a macroscopic system, for instance, for a given density, volume, and total energy. Exactly like the microcanonical ensemble for adiabatic ensembles, the canonical ensemble is only one of the possible choices of isothermal ensembles. And the partition function enables the calculation of all thermodynamic properties of a system. In the microcanonical ensemble, the key parameters are the number of particles, the volume, and the energy. It is actually so famous that it is engraved in Boltzmann’s tombstone in Vienna. The same reasoning applies to adiabatic ensembles like the microcanonical ensemble, with the partition function.
