  Correlation functions are a standard tool for analyzing statistical particle
trajectories. Recently, a so called mean back relaxation (MBR) has been
introduced, which correlates positions at three time points and which has been
shown to be a marker for breakage of time reversal symmetry for confined
particles. Here, we extend this discussion in several ways. We give an
extension to multiple dimensions. Using a path integral approach, we provide a
general expression for MBR in terms of multipoint density correlations. For
Gaussian systems, this expression yields a relation between MBR and mean
squared displacement. From it, several properties of MBR for Gaussian
equilibrium systems can be found, such as monotonicity and positivity.
Unexpectedly, in this case the particle forgets the conditioning via a power
law in time. We finally demonstrate that using MBR for microscopic densities,
it is a marker for broken detailed balance even in bulk systems.
