  This brief note considers the problem of estimating temporal synergy and
integrated information in dyadic dynamical processes. One of the standard
estimators of dynamic synergy is based on the minimal mutual information
between sets of elements, however, despite it's increasingly widespread use,
the mathematical features of this redundancy function have largely gone
unexplored. Here, we show that it has two previously unrecognized limitations:
it cannot disambiguate between truly integrated systems and disintegrated
systems with first-order autocorrelation. Second, paradoxically, there are some
systems that become more synergistic when dis-integrated (as long as
first-order autocorrelations are preserved). In these systems, integrated
information can decrease while synergy simultaneously increases. We derive
conditions under which this occurs and discuss the implications of these
findings for past and future work in applied fields such as neuroscience.
