Efficiency of Sampling: Ergodicity and Autocorrelation Functions

This lecture covers the efficiency of sampling in molecular dynamics and sampling path integral methods. It explains the concept of ergodicity in sampling, focusing on autocorrelation functions as a key tool to measure it. The lecture introduces autocorrelation functions and their role in ensemble averages, illustrating their meaning with examples. It also discusses correlation time and statistical efficiency, emphasizing how autocorrelation time reflects the spacing between uncorrelated samples and impacts the convergence of statistical errors. The take-home message highlights the importance of ergodicity in exploring phase space and the role of autocorrelation functions in indicating correlations and measuring statistical error convergence.