Dynamical Stationarity as a Result of Sustained Random Growth

TL;DR

This paper explores how sustained random growth in complex systems can lead to stationary distributions without detailed balance, indicating thermodynamical behavior, and develops models to describe such phenomena.

Contribution

It introduces a generalized approach using master equations and fluctuation-dissipation principles to model stationary distributions in growing systems.

Findings

Stationary distributions can exist without detailed balance in growing systems.

Derived elementary rates from known stationary distributions.

Reconstructed distributions for networks, citations, and income data.

Abstract

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationary distributions is a generalization of the fluctuation--dissipation theorem. Entropic distance evolution is given for such systems. We reconstruct distributions obtained for growing networks, particle production, scientific citations and income distribution.