A degeneracy factor counts distinct microstates sharing the same specified energy or other grouped quantum labels. If an energy level has multiplicity , its contribution to the canonical partition function is . The probability of occupying that entire level is consequently proportional to both its Boltzmann factor and its state degeneracy.
For a lower nondegenerate level at zero energy and an upper level at with degeneracy factor , the upper-level probability is . Equal level probabilities occur at , rather than necessarily at equal energies. This makes state counting a source of observable entropic shifts. The multiplicity must match what has already been counted explicitly; summing separately over spin states and then multiplying by the same spin multiplicity would double-count microstates.
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