Quantifying time irreversibility using probabilistic differences between symmetric permutations

TL;DR

This paper introduces a subtraction-based parameter, Ys, that quantifies time irreversibility in time series by analyzing probabilistic differences between symmetric permutations, validated on chaotic models, Gaussian processes, and EEG data.

Contribution

It proposes a novel measure, Ys, for time irreversibility based on order patterns and forbidden permutations, enhancing analysis of nonlinear dynamics in complex systems.

Findings

Ys effectively detects time irreversibility in chaotic and Gaussian models.

EEG analysis shows decreased nonlinearity during epileptic seizure-free intervals.

Method proves promising for analyzing nonlinear characteristics in physiological signals.

Abstract

To simplify the quantification of time irreversibility, we employ order patterns instead of the raw multi-dimension vectors in time series, and considering the existence of forbidden permutation, we propose a subtraction-based parameter, Ys, to measure the probabilistic differences between symmetric permutations for time irreversibility. Two chaotic models, the logistic and Henon systems, and reversible Gaussian process and their surrogate data are used to validate the time-irreversible measure, and time irreversibility of epileptic EEGs from Nanjing General Hospital is detected by the parameter. Test results prove that it is promising to quantify time irreversibility by measuring the subtraction-based probabilistic differences between symmetric order patterns, and our findings highlight the manifestation of nonlinearity of whether healthy or diseased EEGs and suggest that the epilepsy leads to a decline in the nonlinearity of brain electrical activities during seize-free intervals.