  We argue that one can model deviations from the ensemble average in
non-equilibrium statistical mechanics by promoting the Boltzmann equation to an
equation in terms of {\em functionals} , representing possible candidates for
phase space distributions inferred from a finite observed number of degrees of
freedom.
  We find that, provided the collision term and the Vlasov drift term are both
included, a gauge-like redundancy arises which does not go away even if the
functional is narrow.
  We argue that this effect is linked to the gauge-like symmetry found in
relativistic hydrodynamics \cite{bdnk} and that it could be part of the
explanation for the apparent fluid-like behavior in small systems in hadronic
collisions and other strongly-coupled small systems\cite{zajc}.
  When causality is omitted this problem can be look at via random matrix
theory show, and we show that in such a case thermalization happens much more
quickly than the Boltzmann equation would infer. We also sketch an algorithm to
study this problem numerically
