Mixing Rates of Ergodic Algorithms

Abstract: In response to the 2024 Snook Prize Problem, this paper compares the mixing rates of six simple numerical algorithms that produce an ergodic Gaussian distribution of position and momentum for a one-dimensional harmonic oscillator. A hundred thousand initial conditions spread uniformly over the constant energy surface are used for each of the six systems. The time-dependent kurtosis serves as a measure of the mixing rate. By this criterion, the most rapid mixing occurs for the signum thermostat system with an optimally chosen parameter value.