The study of autocorrelation times of various meson operators and the topological charge revealed the presence of hidden harmonic oscillations of the autocorrelations (for the HMC).
These modes can be extracted by smoothing the observables with respect to the Monte Carlo time. While this smoothing procedure removes the largest share of the operator's signal, it can not be excluded that physically relevant contributions remain coupled to the oscillations. Furthermore, common statistical error analysis relies on binning and, thus, is not suited to remove non-decaying forms of autocorrelation.
I present a new error analysis framework that is based on defining an effective number of independent measurements via the ratio of the entropy of the correlated data distribution excluding autocorrelation and the entropy of the distribution including autocorrelation.
This framework is used to show that the autocorrelation oscillations are significant. I argue that the oscillations could be understood in terms of a 5D theory involving the Molecular dynamics momenta and are manifestations of the theoretical modes used by the Fourier acceleration approach. FA might control the modes and suppress their impact on the simulated physics.