Comparison of the serial and parallel algorithms of generalized ensemble simulations: An analytical approach

This paper addresses issues related to weights and acceptance rates in generalized ensemble simulations, while comparing two algorithms: serial (e.g., simulated tempering or expanded ensemble method) and parallel (e.g., parallel tempering or replica exchange). We derive a cumulant approximation for weights and discuss its effectiveness in practical applications. We compare the acceptance rates of the serial and parallel algorithms and prove that the serial algorithm always has higher acceptance rates. The duality between forward and backward transitions plays a crucial role in the derivations throughout the paper.