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Although time irreversibility (TIR) and amplitude irreversibility (AIR) arerelevant concepts for nonequilibrium analysis, their association has receivedlittle attention. This paper conducts a systematic comparative analysis of therelationship between TIR and AIR based on statistical descriptions andnumerical simulations. To simplify the quantification of TIR and AIR, theamplitude permutation and global information of the associated vector arecombined to produce a joint probability estimation. Chaotic logistic, Henon,and Lorenz series are generated to evaluate TIR and AIR according to surrogatetheory, and the distributions of joint permutations for these model series aremeasured to compare the degree of TIR and AIR. The joint permutation TIR andAIR are then used to investigate nonequilibrium pathological features inepileptic electroencephalography data. Test results suggest that epilepticbrain electrical activities, particular those during the onset of seizure,manifest higher nonequilibrium characteristics. According to the statisticaldefinitions and targeted pairs of joint permutations in the chaotic model data,TIR and AIR are fundamentally different nonequilibrium descriptors from time-and amplitude-reversibility, respectively, and thus require different forms ofnumerical analysis. At the same time, TIR and AIR both provide measures forfluctuation theorems associated with nonequilibrium processes, and have similarprobabilistic differences in the pairs of joint permutations and consistentoutcomes when used to analyze both the model series and real-world signals.Overall, comparative analysis of TIR and AIR contributes to our understandingof nonequilibrium features and broadens the scope of quantitativenonequilibrium measures. Additionally, the construction of joint permutationscontributes to the development of symbolic time series analysis.

Comparative analysis of time irreversibility and amplitude irreversibility based on joint permutation