Measuring the irreversibility of numerical schemes for reversible stochastic differential equations (Q2925703)

The entropy production rate (EPR) is used to estimate the loss of reversibility when approximations of the solution of a reversible stochastic differential equation are generated using a numerical method. This analysis is applied to the overdamped Langevin equation to determine that the explicit Euler-Maruyama method yields order \(\Delta t^2\) decrease of the EPR in the case of additive noise, but the EPR is not reduced by reducing the stepsize \(\Delta t\) in the case of multiplicative noise.NEWLINENEWLINE However, the explicit Milstein method is shown to yield order \(\Delta t\) decrease in the EPR in the case of multiplicative noise. The BBK integrator is shown to yield order \(\Delta t\) decrease in the EPR when applied to a Langevin system with additive noise.