  A theory of intermittency differentiation is developed for a general class of
1D Infinitely Divisible Multiplicative Chaos measures. The intermittency
invariance of the underlying infinitely divisible field is established and
utilized to derive a Feynman-Kac equation for the distribution of the total
mass of the limit measure by considering a stochastic flow in intermittency.
The resulting equation prescribes the rule of intermittency differentiation for
a general functional of the total mass and determines the distribution of the
total mass and its dependence structure to the first order in intermittency. A
class of non-local functionals of the limit measure extending the total mass is
introduced and shown to be invariant under intermittency differentiation making
the computation of the full high temperature expansion of the total mass
distribution possible in principle. For application, positive integer moments
and covariance structure of the total mass are considered in detail.
