Superstatistics from a different perspective

TL;DR

This paper offers a new perspective on superstatistics, suggesting that the observed unconventional statistics can result from the intrinsic dynamics of the system itself, rather than solely from background fluctuations.

Contribution

It proposes that the same superstatistical formalism can be derived from the system's intrinsic dynamics, providing a different conceptual understanding.

Findings

Different systems within the same background can produce varied statistics.

A toy model demonstrates the emergence of power-law distributions.

Supporting recent results align with the intrinsic dynamics perspective.

Abstract

In this paper we elaborate on the recently proposed superstatistics formalism [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)], used to interpret unconventional statistics. Their interpretation is that unconventional statistics in dynamical systems arise as weighted averages of the ordinary statistics obeyed by these systems over a statistical distribution of background configurations due to fluctuations intrinsic to the background. In this paper we suggest that the same picture can arise because of the intrinsic dynamics of the system. The dynamics of the system and the background, hence, concur together to determine the overall final statistics: differently evolving systems embedded within the same background can yield different statistical distributions. Some simple examples are provided; among them a toy model able to yield a power-law distribution. Also, some recent independent results are quoted, that appear to support this viewpoint.