  Time irreversibility (temporal asymmetry) is one of fundamental properties
that characterize the nonlinearity of complex dynamical processes, and our
brain is a typical complex dynamical system manifested with nonlinearity. Two
subtraction-based parameters, Ys and X2, are employed to measure the
probabilistic differences of permutations instead of raw vectors for the
simplified quantification of time irreversibility, which is validated by
chaotic and reversible processes and the surrogate data. We show that it is
equivalent to quantify time irreversibility by measuring probabilistic
difference between the forward and its backward processes and between the
symmetric permutations. And we detect time irreversibility of two groups of
epileptic EEGs, from the Nanjing General Hospital (NJGH) and from the public
Bonn epileptic database. In our contribution, NJGH epileptic EEGs during
seizure-free intervals of have lower time irreversibility than the control data
while those of the Bonn data sets have higher nonlinearity than the healthy
brain electrical activities. For the inconsistent results, we conduct
multi-scale analysis and elucidate from the circadian rhythms in epileptic
nonlinearity, however, more targeted researches are needed to verify our
assumptions or to determine if there are other reasons leading to the
inconsistency.
