Microcanonical Ensemble - The Microcanonical Ensemble

The Microcanonical Ensemble

In the microcanonical ensemble, all copies, or distinct microstates, of the system have the same number of particles (N), the same volume (V) and the same energy (E). This is precisely what distinguishes an isolated system. If is the number of accessible microstates, the probability that a system chosen at random from the ensemble would be in a given microstate is simply . It is possible to approximately calculate for a number of systems such as the ideal gas, the 2-state paramagnet, and the Einstein Solid.

The benefit of the ensemble is that it allows for calculation of average values for thermodynamic properties. For example, while the pressure of a container of gas fluctuates continuously, we measure the time average of the pressure. The ensemble contains all microstates which the system might inhabit during the period of measurement, so we can replace the time average with an average over the ensemble. Systems for which this is possible are called ergodic.