  Although time irreversibility (TIR) and amplitude irreversibility (AIR) are
relevant concepts for nonequilibrium analysis, their association has received
little attention. This paper conducts a systematic comparative analysis of the
relationship between TIR and AIR based on statistical descriptions and
numerical simulations. To simplify the quantification of TIR and AIR, the
amplitude permutation and global information of the associated vector are
combined to produce a joint probability estimation. Chaotic logistic, Henon,
and Lorenz series are generated to evaluate TIR and AIR according to surrogate
theory, and the distributions of joint permutations for these model series are
measured to compare the degree of TIR and AIR. The joint permutation TIR and
AIR are then used to investigate nonequilibrium pathological features in
epileptic electroencephalography data. Test results suggest that epileptic
brain electrical activities, particular those during the onset of seizure,
manifest higher nonequilibrium characteristics. According to the statistical
definitions 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 of
numerical analysis. At the same time, TIR and AIR both provide measures for
fluctuation theorems associated with nonequilibrium processes, and have similar
probabilistic differences in the pairs of joint permutations and consistent
outcomes when used to analyze both the model series and real-world signals.
Overall, comparative analysis of TIR and AIR contributes to our understanding
of nonequilibrium features and broadens the scope of quantitative
nonequilibrium measures. Additionally, the construction of joint permutations
contributes to the development of symbolic time series analysis.
