A constant entropy increase model for the selection of parallel tempering ensembles

Abstract

The present paper explores a simple approach to the question of parallel tempering temperature selection. We argue that to optimize the performance of parallel tempering it is reasonable to require that the increase in entropy between successive temperatures be uniform over the entire ensemble. An estimate of the system's heat capacity, obtained either from experiment, a preliminary simulation, or a suitable physical model, thus provides a means for generating the desired tempering ensemble. Applications to the two-dimensional Ising problem indicate that the resulting method is effective, simple to implement, and robust with respect to its sensitivity to the quality of the underlying heat capacity model.

Comparative study of selected parallel tempering methods

“…The second method of selection of the PT temperature sequence, requires a constant increase in entropy between successive temperatures [41]. To describe this method we follow Sabo et al [41] and denote the M temperatures of the CEI sequence by (T m ; m = 1, ..., M ) and the total increase in entropy from T 1 to T M by ∆S.…”

“…There is a rather large number of ideas that have been proposed in the last decade to resolve this question [40][41][42][43][44][50][51][52][53]. According to the approach followed by Katzgaber et al [53], optimal temperatures correspond to a maximum rate of round trips between low and high temperatures in temperature space and can be obtained using a recursive readjustment of temperatures.…”

“…The second method, for the selection of temperatures, was introduced by Sabo et al [41]. This method requires a constant increase in entropy between successive temperatures.…”

Parallel-Tempering Monte-Carlo Simulation with Feedback-Optimized Algorithm Applied to a Coil-to-Globule Transition of a Lattice Homopolymer

“…We do not vary the exchange interval, S, which is set to 200 MCS. In the future, we intend to test the S effect on the PT simulation results.It is worth to notice, that there are also other methods for generating optimal temperature sets [8][9][10]. One of them, is proposed by Sabe et al [9], and is based mainly on the work of Kofke [11] and Kone and Kofke [12], in which the optimal temperature sets are found by using the condition of constant entropy increase for the adjacent replicas.…”

“…One of them, is proposed by Sabe et al [9], and is based mainly on the work of Kofke [11] and Kone and Kofke [12], in which the optimal temperature sets are found by using the condition of constant entropy increase for the adjacent replicas. According to our knowledge, the round-trip time of replicas with the FOPT, which we present in this work, is used as a criterion for finding optimal number of replicas in the PT simulations for the first time.…”