Emergence of pseudo-time during optimal Monte Carlo sampling and temporal aspects of symmetry breaking and restoration

Abstract

We argue that one can associate a pseudo-time with sequences of configurations generated in the course of classical Monte Carlo simulations for a single-minimum 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 pseudo-time as a quantity emerging together with the bound state. Conversely, when transport among distinct bound states takes place -- thus restoring symmetry -- a pseudo-time can no longer be defined. One can still quantify activation barriers, if the latter barriers are smooth, but the simulation becomes impractically slow and pertains to overdamped transport only. Specially designed Monte Carlo moves that bypass activation barriers -- so as to accelerate sampling of the thermodynamics -- amount to effusive transport and lead to severe under-sampling of transition-state configurations that separate distinct bound states while destroying the said universality. Implications of the present findings for simulations of glassy liquids are discussed.

References in corpus (21)

• Theory of Structural Glasses and Supercooled Liquids
• Diffusive Dynamics of the Reaction Coordinate for Protein Folding Funnels
• The structural glass transition and the entropy of the metastable states
• Fragilities of Liquids Predicted from the Random First Order Transition Theory of Glasses
• Models and algorithms for the next generation of glass transition studies
• Stripe glasses: self generated randomness in a uniformly frustrated system
• Theory of Aging in Structural Glasses
• The Monte-Carlo dynamics of a binary Lennard-Jones glass-forming mixture
• Thirty milliseconds in the life of a supercooled liquid
• Modern computational studies of the glass transition
• Efficient swap algorithms for molecular dynamics simulations of equilibrium supercooled liquids
• Bound States in one and two Spatial Dimensions
• Theory of the Structural Glass Transition: A Pedagogical Review
• Can the glass transition be explained without a growing static length scale?
• Dynamical Mean Field Theory for Self-Generated Quantum Glasses
• Droplets and the configurational entropy crisis for random first order transitions
• Stress distribution and the fragility of supercooled melts
• The chemical bond as an emergent phenomenon
• Electronic structure and the glass transition in pnictide and chalcogenide semiconductor alloys. Part II: The intrinsic electronic midgap states
• Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids
• Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids

Cited by in corpus (1)

• Cavitation in Electron Fluids and the Puzzles of Photoemission Spectra in Alkali Metals