  We have introduced a variational method to improve the computation of
integrated correlation times in the Parallel Tempering Dynamics, obtaining a
better estimate (a lower bound, at least) of the exponential correlation time.
Using this determination of the correlation times, we revisited the problem of
the characterization of the chaos in temperature in finite dimensional spin
glasses by means of the study of correlations between different chaos
indicators computed in the static and the correlation times of the Parallel
Tempering dynamics. The sample-distribution of the characteristic time for the
Parallel Tempering dynamics turns out to be fat-tailed and it obeys finite-size
scaling.
