  A multicanonical formalism is introduced to describe statistical equilibrium
of complex systems exhibiting a hierarchy of time and length scales, where the
hierarchical structure is described as a set of nested "internal heat
reservoirs" with fluctuating "temperatures." The probability distribution of
states at small scales is written as an appropriate averaging of the
large-scale distribution (the Boltzmann-Gibbs distribution) over these
effective internal degrees of freedom. For a large class of systems the
multicanonical distribution is given explicitly in terms of generalized
hypergeometric functions. As a concrete example, it is shown that generalized
hypergeometric distributions describe remarkably well the statistics of
acceleration measurements in Lagrangian turbulence.
