Dynamics and optimal number of replicas in parallel tempering simulations

We study the dynamics of parallel tempering simulations, also known as the replica exchange technique, which has become the method of choice for simulation of proteins and other complex systems. Recent results for the optimal choice of the control parameter discretization allow a treatment independent of the system in question. By analyzing mean first passage times across the control parameter space, we find an expression for the optimal number of replicas in simulations covering a given temperature range. Our results suggest a particular protocol to optimize the number of replicas in actual simulations.

Figure 1

Different functional forms for the decay of the transition probability with control parameter distance; compare Eqs. (7, 13).

Figure 2

Dependence of relative mean first passage time, Eq. (12), on deviations from the optimal number of replicas for the different functions of Eq. (13).