Comment on 'Preserving the Boltzmann ensemble in replica-exchangemolecular dynamics' J. Chem. Phys. 129, 164112 (2008)

摘要

In a recent paper,~1 the basic concepts of constant tem-perature molecular dynamics (CTMD) were criticized;replica-exchange molecular dynamics~2(REMD) was alsocriticized since studies of REMD employ CTMD techniques.Among the criticisms,~3I here address the issue regardinggeneral theoretical aspects of Nose-Hoover~(4'5)(NH) and re-lated methods. Specifically, in Secs. VB and VC of Ref. 1, itis stated in mathematical manners that (I) the NH equation isnot measure-preserving~6(MP);(H)the NH and chainsystems are not ergodic under the Boltzmann-Gibbs (BG)measure; and (III) the Nose Hamiltonian system (HS) as wellas the Nose-Poincare~8(NP) HS is not ergodic. The MP prop-erty is the starting point for discussing the ergodic theory,~9which deals with the transformations that preserve the struc-tures of measure spaces. MP also implies maintaining theprobability of a set of states at constant value and is criticalfor inducing the compatibility between the MD equation andthe BG distribution, owing to the existence of a measureassociate with the BG density factor. The ergodicity explainsthat the time series via MD leads to the BG ensemble. Ifstatements (I)-(III) are completely true, then the typicalCTMD above may not produce the correct BG ensemble,and then the basis of not only the REMD but many othertechniques, including generalized-ensemble methods, is un-dermined, leading to the suspicion of the correctness ofmany simulation results. This study demonstrates, by a math-ematical standpoint, that (I) is misleading, (II) is not provedsince the argument in Ref. 1 is incorrect, and (III) is notproved in a meaningful sense and the proof of (III) in Ref. 1does not imply the failure of the production of the BG en-semble in these two HSs.