Consider a collection of N non-interacting particles. Each particle can be in one of R states. Themicrocanonical ensemble assumption states that, left to itself, the system will visit all allowed microstates with equal probability. The allowed microstates correspond to all the different ways one can allocate the R states to the N particles under the given constraints. Let ni denote the number of particles in state i. If there were no constraints there would be a total of

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2(n) N! m! n!...nR! microstates corresponding to the configuration n = (n,n,n). (n) varies greatly depending on the configuration. For example, there is only one microstate for n = (N,0,...,0), but many with n = (N/R,...,N/R) (assuming N to be divisible by R). It is therefore sensible to assume that the configurations n in which one typically finds the system correspond to the largest number of allowed microstates. That is, the configuration that maximises 2(n) under the constraints given by the particle number R n = N i=1 () and total energy R n = U. () i=1