Ergodicity in statistical mechanics roughly means that you can replace an average over time by an average over states. In practice this means that within the t

Ergodicity in statistical mechanics roughly means that you can replace an average over time by an average over states. In practice this means that within the time it takes to perform your measurement the system should move through a lot of “typical” states. So for everything that matters: If statistical mechanics works you can conclude that the system is ergodic. And if you observe long-time correlations it’s not.