On supercorrelated systems and phase space entrainment

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 one-dimensional 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.