Define the participation ratio as Y = ∑ ∑ E p E 2 = ∑ ∑ E e − − 2 β β E ( ∑ ∑ E e − − β β E ) 2 The participation ratio measures the amount of condensation in the Boltzmann distribution. It can be interpreted as the probability that two randomly sampled states are exactly the same state. Indeed, it is precisely the Simpson index, a commonly used diversity index.