Emergence of pseudotime during optimal Monte Carlo sampling and temporal aspects of symmetry breaking and restoration
Abstract
We argue that one can associate a pseudotime with sequences of configurations generated in the course of classical Monte Carlo simulations for a singleminimum bound state if the sampling is optimal. Hereby, the sampling rates can be, under special circumstances, calibrated against the relaxation rate and frequency of motion of an actual physical system. The latter possibility is linked to the optimal sampling regime being a universal crossover separating two distinct suboptimal sampling regimes analogous to the physical phenomena of diffusion and effusion, respectively. Bound states break symmetry; one may thus regard the pseudotime as a quantity emerging together with the bound state. Conversely, when transport among distinct bound states takes placethus restoring symmetrya pseudotime can no longer be defined. One can still quantify activation barriers if the latter barriers are smooth, but simulation becomes impractically slow and pertains to overdamped transport only. Specially designed Monte Carlo moves that bypass activation barriersso as to accelerate sampling of the thermodynamicsamount to effusive transport and lead to severe undersampling of transitionstate configurations that separate distinct bound states while destroying the said universality. Implications of the present findings for simulations of glassy liquids are discussed.
 Publication:

Journal of Chemical Physics
 Pub Date:
 March 2023
 DOI:
 10.1063/5.0135479
 arXiv:
 arXiv:2305.16603
 Bibcode:
 2023JChPh.158l4119H
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 published in J. Chem. Phys. 158, 124119 (2023)