Applied Modeling Techniques and Data Analysis 2

16Revisiting Transitions Between Superstatistics

This work aims to provide an accurate method for the detection of a transition between superstatistics. A slight improvement over the currently published method is achieved. The superstatistics framework is briefly recalled and a rather new concept of the transition of superstatistics, introduced by Xu and Beck (2016), is re-examined. In addition, an original synthetic model for superstatistical transition, suggested by Beck, is discussed. It is shown that its modified version, which takes into account a stochastic nature of the transition, better reflects empirically observed transitions.

16.1. Introduction

Superstatistics is a well-known term in the field of non-equilibrium statistical physics. It describes a system in a local thermodynamic equilibrium. However, only recently, a new spin in the superstatistical paradigm has been introduced, namely, a transition of superstatistics (Xu and Beck 2016). Its application is predominantly in time series analysis. The basic premise is that the superstatistical smearing distribution may change on different time scales. The first experimental evidence for this phenomenon was introduced by Xu and Beck (2016). The pioneering paper was followed by our paper (Jizba et al. 2018) which introduced a more reliable method for detecting the alleged transition. The method was based on leveraging statistical distances in order to decide a favorable probability distribution on various time scales. ...