Measuring dynamical phase transitions in time series

TL;DR

This paper introduces a new method for detecting dynamical phase transitions in time series by measuring the derivative of the Rényi-entropy spectrum, providing a computationally efficient predictor for bifurcation points.

Contribution

It derives a closed-form expression for the derivative of the Rényi-entropy spectrum within Markov processes, enabling better detection of phase transitions in chaotic systems.

Findings

The measure can predict dynamical phase transitions in various systems.

The method is computationally efficient and applicable to real-world data.

Limitations include sensitivity to noise and system complexity.

Abstract

There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the underlying chaotic systems is a notoriously difficult task. Building on prior theoretical studies that focus on the discontinuities at $q=1$ in the order-$q$ R\'enyi-entropy of the trajectory space, we measure the derivative of the spectrum. We derive within the general context of Markov processes a computationally efficient closed-form expression for this measure. We investigate its properties through well-known dynamical systems exploring its scope and limitations. The proposed mathematical instrument can serve as a predictor of dynamical phase transitions in time series.