Quantifying time irreversibility using probabilistic differences between symmetric permutations

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, $Y_S$, 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.