  Focusing on non-ergodic macroscopic systems we reconsider the variances of
time averages time-series. The total variance (direct average over all
time-series) is known to be the sum of an internal variance (fluctuations
within the meta-basins) and an external variance (fluctuations between
meta-basins). It is shown that whenever the time-averaged observable can be
expressed as a volume average of a local field the three variances can be
written as volume averages of correlation functions with the total correlation
function being the sum of an internal and an external correlation function. The
dependences of the the different variancescan thus be traced back to the
internal and the external correlation function. Various relations are
illustrated using lattice spring models with spatially correlated spring
constants.
