We present JeLLyFysh-Version1.0, an open-source Python application for eventchain Monte Carlo (ECMC), an event-driven irreversible Markov-chain Monte Carlo algorithm for classical N -body simulations in statistical mechanics, biophysics and electrochemistry. The application's architecture closely mirrors the mathematical formulation of ECMC. Local potentials, long-ranged Coulomb interactions and multi-body bending potentials are covered, as well as bounding potentials and cell systems including the cell-veto algorithm. Configuration files illustrate a number of specific implementations for interacting atoms, dipoles, and water molecules.

No abstract

We propose locally stable sparse hard-disk packings, as introduced by Böröczky, as a model for the analysis and benchmarking of Markov-chain Monte Carlo (MCMC) algorithms. We first generate such Böröczky packings in a square box with periodic boundary conditions and analyze their properties. We then study how local MCMC algorithms, namely the Metropolis algorithm and several versions of event-chain Monte Carlo (ECMC), escape from configurations that are obtained from the packings by slightly reducing all disk radii by a relaxation parameter. We obtain two classes of ECMC, one in which the escape time varies algebraically with the relaxation parameter (as for the local Metropolis algorithm) and another in which the escape time scales as the logarithm of the relaxation parameter. A scaling analysis is confirmed by simulation results. We discuss the connectivity of the hard-disk sample space, the ergodicity of local MCMC algorithms, as well as the meaning of packings in the context of the NPT ensemble. Our work is accompanied by open-source, arbitrary-precision software for Böröczky packings (in Python) and for straight, reflective, forward, and Newtonian ECMC (in Go).