The needed number of nodes n in a HREM simulation depends on the total number of degrees of freedom N involved in the scaling. As the mean potential energy Ē and its variance δE 2 are extensive functions, the larger is the number of degrees of freedom N involved in the scaling, the more states will be necessary for a significant overlap of contiguous distributions with n ∝ E δE ∝ N 1/2 . The tuning of an HREM simulation for optimal sampling efficiency is by no means a trivial task. As shown in Ref., the exchange attempt frequency (EAF), one of the parameters of an HREM simulation, should be chosen as high as possible (typically 0.03-0.05 ps -1 ) provided that the communication cost of the attempted exchange in a parallel execution is small as it happens when we exchange scaling factors rather than configurations. High P acc (k) are in principle desirable but they are costly as they involve a large n. Like in standard Monte Carlo, it is generally believed that an optimal (and balanced) P acc (k) in systems with kinetics traps should be in the range 0.2-0.5. Balancing the acceptance probabilities P acc (k) may, in general, result in a smoother replica diffusion and in a shortening of the round trip times (RTT). On the other hand, as noted in Ref., well balanced acceptance ratios along the states progression does not guarantee an optimal flux in HREM simulation. The upward flux can be measured as