If we were to run two simulations at temperatures separated by a Δ T, we would find that if Δ T is small enough, then the energy histograms obtained by collecting the values of the energies over a set of Monte Carlo steps N will create two distributions that will somewhat overlap. The overlap can be defined by the area of the histograms that falls over the same interval of energy values, normalized by the total number of samples. For Δ T = 0 the overlap should approach 1.