  It has been recently noted that for a class of dynamical systems with
explicit conservation laws represented via projector operators the dynamics can
be understood in terms of lower dimensional equations This is the case for
instance of memristive circuits Memristive systems are important classes of
devices with wide ranging applications in electronic circuits artificial neural
networks and memory storage We show that such mean field theories can emerge
from averages over the group of orthogonal matrices interpreted as cycle
preserving transformations applied to the projector operator describing
Kirchhoffs laws Our results provide insights into the fundamental principles
underlying the behavior of resistive and memristive circuits and highlight the
importance of conservation laws for their meanf ield theories In addition we
argue that our results shed light on the nature of the critical avalanches
observed in quasi-two dimensional nanowires as boundary phenomena
