Some authors prefer to view the microcanonical ensemble as being the more fundamental, the canonical ensemble being derived from the microcanonical. These Lectures follow an alternative approach, taking the canonical ensemble as being the most fundamental. A major argument in favor of eq. The importance of simplicity, and the relative merits of largely equivalent equations, are matters of theology. Whether one begins with the canonical or the microcanonical ensemble, one needs the same number of assumptions and special entities to obtain thermodynamic behavior, so the usual form of Occam's razor will not separate them.
Some sources claim that eq.
3.4 can be derived from theoretical considerations. The usual argument is that the Law of Equal a priori Probabilities must be correct, because there is no reason for any state to be preferred to any other . Furthermore, could have a non-trivial functional dependence on those variables that differ from state to state, in which case some states could be preferred to some other states. Furthermore, the italicized argument for the Law of Equal a priori Probabilities has no feature which causes the argument to refer specifically to the microcanonical ensemble. However, of the canonical ensemble is not a constant, so the argument must be wrong for the canonical ensemble.