Two-dimensional binary Lennard-Jones mixtures with ECMC

We discuss reversible and non-reversible local Monte Carlo algorithms for long-range two-dimensional binary Lennard-Jones mixtures. We illustrate how the factorized Metropolis filter efficiently handles long-range interactions even for binary mixtures, using an adapted cell-veto strategy. We then benchmark the non-reversible event-chain Monte Carlo (ECMC) algorithm against the factorized Metropolis algorithm. For simple test cases, we demonstrate speedups of several orders of magnitude in the equilibrium and the out-of-equilibrium dynamics. Using the ECMC algorithm, we provide an overview of the physics of binary Lennard-Jones mixtures, from the case without depletion (no interaction between solute and solvent) all the way to the depletion limit (with a diverging number of solvent particles). We analyze the algorithms in different thermodynamic phases and in the corresponding limits.