  In a recent article (J. Comput. Chem. 2013, 34, 132-140), convective
Replica-Exchange (convective-RE) has been presented as an alternative to the
standard even-odd transition scheme. Computations on systems of various
complexity have shown that convective-RE may increase the number of replica
round-trips in temperature space with respect to the standard exchange scheme,
leading to a more effective sampling of energy basins. Moreover, it has been
shown that the method may prevent the formation of bottlenecks in the diffusive
walk of replicas through the space of temperature states. By using an ideal
temperature-RE model and a classical harmonic-oscillator RE scheme, we study
the performances of convective-RE when ergodicity is not broken and convergence
of acceptance probabilities is attained. In this dynamic regime, the round-trip
ratio between convective and standard-RE is at maximum ~1.5, a value much
smaller than that observed in non-ergodic simulations. For large acceptance
probabilities, the standard-RE outperforms convective-RE. Our observations
suggest that convective-RE can safely be used in either ergodic or non ergodic
regimes; however, convective-RE is advantageous only when bottlenecks occur in
the state-space diffusion of replicas, or when acceptance probabilities are
globally low. We also show that decoupling of the state-space dynamics of the
stick replica from the dynamics of the remaining replicas improves the
efficiency of convective-RE at low acceptance probability regimes.
