  It is demonstrated that power-laws which are modified by logarithmic
corrections arise in supercorrelated systems. Their characteristic feature is
the energy attributed to a state (or value of a general cost function) which
depends nonlinearly on the phase space distribution of the constituents. A
onedimensional dissipative deterministic model is introduced which is attracted
to a supercorrelated state (phase space entrainment). Extensions of this
particular model may have applications in the study of transport and
equilibration phenomena, particularly for supply and information networks, or
for chemical and biological nonequilibrium systems, while the qualitative
arguments presented here are believed to be of more general interest.
