  The nature of the electron gas is characterized, above all, by its
multi-particle correlations. The conserving sum rules for the electron gas have
been thoroughly studied for many years, and their centrality to the physics of
metallic conduction is widely understood (at least in the many-body community).
We review the role of the conserving sum rules in mesoscopic transport, as
normative criteria for assessing the conserving status of mesoscopic models. In
themselves, the sum rules are specific enough to rule out any such theory if it
fails to respect the conservation laws. Of greater interest is the capacity of
the compressibility sum rule, in particular, to reveal unexpected fluctuation
effects in nonuniform mesoscopic structures.
