We present results for the nonequilibrium dynamics of collapse for a model flexible homopolymer on simple cubic lattices with fixed and fluctuating bonds between the monomers. Results from our Monte Carlo simulations show that, phenomenologically, the sequence of events observed during the collapse are independent of the bond criterion. While the growth of the clusters (of monomers) at different temperatures exhibits a nonuniversal power-law behavior when the bonds are fixed, the introduction of fluctuations in the bonds by considering the existence of diagonal bonds produces a temperature independent growth, which can be described by a universal nonequilibrium finite-size scaling function with a non-universal metric factor. We also examine the related aging phenomenon, probed by a suitable two-time density-density autocorrelation function showing a simple power-law scaling with respect to the growing cluster size. Unlike the cluster-growth exponent α c , the nonequilibrium autocorrelation exponent λ C governing the aging during the collapse, however, is independent of the bond type and strictly follows the bounds proposed by two of us in Phys. Rev. E 93, 032506 (2016) at all temperatures.

Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse using computer simulations. Primary focus of these approaches is to understand various dynamical scaling laws related to coarsening and aging during the collapse in space dimension d = 3, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overview of those results, we also present new preliminary data for d = 2.

We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions perform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.Generic models of statistical physics exhibiting a transition from disordered to ordered states have been proved to be instrumental for understanding the dynamics in diverse fields, from species evolution [1] to traffic flow [1], from economic dynamics [2] to rainfall dynamics [3]. An extensively used paradigm is the Ising model with nearest-neighbor (NNIM) interaction [4,5]. Even the complex neural dynamics of brain depends on similar underlying mechanisms [6]. The maximum entropy models obtained from experimental data upon mapping the spiking activities of the neurons onto spin variables are equivalent to Ising models [7]. However, it is believed that the neuron activities are effectively modelled by longdistance communications [6]. In nature, also many other intermolecular interactions are evidently long-range, e.g., electrostatic forces, polarization forces, etc. Hence, a more complete picture calls for employing models that consider long-range interactions.The simplest generic model system is the long-range Ising model (LRIM), which on a d-dimensional lattice is described by the Hamiltonian

Population annealing is a powerful tool for large-scale Monte Carlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.Simulations of complex systems with rugged freeenergy landscapes are among the computationally most challenging problems [1]. Next to structural and spin glasses, macromolecules including proteins are prototypical examples of systems were frustration results in many (free) energy minima separated by barriers. A range of methods has been developed to overcome the problem of the system getting trapped in a local minimum [2][3][4][5]. The most popular choice is parallel tempering [3,6,7] (also known as replica exchange) which has been shown to successfully sample a broad configuration space when applied to peptides [8,9]. This method uses a small number of replicas which are, a priori, simulated independently at different temperatures. At regular intervals the replicas exchange configurations with a probability adjusted to their relative Boltzmann weight. Although this approach is easily parallelized, the number of processors that can be reasonably used is limited by the increasing time it takes for a system to traverse the whole temperature range when the number of temperature points increases.Population annealing [10-15] is another generalizedensemble simulation scheme, which was originally introduced for Monte Carlo simulations. While it was found to be similarly good at dealing with complex free-energy landscapes, it can easily make use of many thousands of processors including GPUs [16] and scales extremely well. The approach is based on the ideas of sequential Monte Carlo methods. It consists of setting up an ensemble of R independent configurations at a high temperature where equilibration is straightforward. The population is then sequentially cooled in small steps. At each temperature, the population is resampled according to a ratio of Boltzmann weights and then evolved for a number of simulation steps. This keeps the population in equilibrium and thus observables can be calculated as population averages at each temperature. Parallelization is over independent replicas, and this allows for the good scaling properties as population sizes R as large as 10 6 and beyond are not uncommon. Population annealing has been shown to perform well, e.g., in Monte Carlo simulations of spin glasses [11,13]. Here we show how it can be adapted to molecular dynamics si...

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