Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

TL;DR

This paper explores how power-law distributions naturally emerge in coupled dynamic-stochastic systems through maximum entropy principles and superstatistics, highlighting the role of global constraints and non-equilibrium steady states.

Contribution

It demonstrates that power-law statistics can result from global constraints within a maximum entropy framework applied to coupled systems.

Findings

Power-law dependencies arise from constraints on phase space and fluctuations.

Power-law distributions are linked to non-equilibrium steady states.

Deviation from exponential statistics quantifies non-equilibrium conditions.

Abstract

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a non-equilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.