Scale properties as a basis of power law relaxation processes

TL;DR

This paper demonstrates that first-order relaxation processes governed by scale-invariant interactions naturally evolve into stationary power-law regimes, with derived scaling laws and invariants characterizing their dynamics.

Contribution

It establishes a theoretical link between scale properties of interactions and the emergence of power-law relaxation behaviors in first-order processes.

Findings

Relaxation processes with scale-invariant interactions lead to power-law stationary states.

A scaling law for the time evolution of such systems is derived.

Invariant properties of the relaxation dynamics are identified.

Abstract

Computer simulations of first-order relaxation processes show that the spatial configurations of the system acquire an invariant shape once the stationary regime is attained. Inspired by them we find that, in any first-order relaxation process, if the interaction that governs the system fulfils a simple scale property, then the relaxation will end up by following a stationary process described by a power law. A scaling law and some invariants are obtained for the time evolution of the system in such a case.