A mechanism is proposed for the appearance of power-law
distributions in various complex systems. It is shown that when a system can
be modeled as a dimensionally heterogeneous system (e.g. a conservative
mechanical system composed of subsystems with different numbers of degrees
of freedom) a robust power-law tail appears in the aggregate equilibrium
energy distribution. 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 (which is applied to derive the Zipf law
in linguistics) and a kinetic model of wealth exchange (leading to a Pareto
power-law in the wealth distribution).