Another way to interpret this overlap is to say that system configurations sampled at temperature T 1 are likely to appear during a simulation at T 2. Because the Markov chain should have no memory of its past, we can create a new update for the system composed of the two systems at T 1 and T 2. At a given Monte Carlo step we can update the global system by swapping the configuration of the two systems, or alternatively trading the two temperatures. The update is accepted according to the Metropolis–Hastings criterion with probability