  A mechanism is proposed for the appearance of power law distributions in
various complex systems. It is shown that in a conservative mechanical system
composed of subsystems with different numbers of degrees of freedom a robust
power-law tail can appear in the equilibrium distribution of energy as a result
of certain superpositions of the canonical equilibrium energy densities of the
subsystems. The derivation only uses a variational principle based on the
Boltzmann entropy, without assumptions outside the framework of canonical
equilibrium statistical mechanics. Two examples are discussed, free diffusion
on a complex network and a kinetic model of wealth exchange. The mechanism is
illustrated in the general case through an exactly solvable mechanical model of
a dimensionally heterogeneous system.
