On supercorrelated systems and phase space entrainment

TL;DR

This paper explores supercorrelated systems where energy depends nonlinearly on phase space distribution, leading to power-laws with logarithmic corrections, and introduces a model demonstrating phase space entrainment with potential applications in various complex systems.

Contribution

It introduces a deterministic model that exhibits phase space entrainment in supercorrelated systems, highlighting the emergence of modified power-law distributions.

Findings

Power-laws with logarithmic corrections arise in supercorrelated systems.

A one-dimensional dissipative model demonstrates phase space entrainment.

Potential applications in transport, chemical, and biological systems.

Abstract

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.