Before revision: Time irreversibility, a fundamental property of complex system, can be characterized by the directional asymmetry of probabilistic distributions, which is quantified by equalities-involved permutation relative entropy in our nonlinear dynamics analysis of heart rates . Equal values are not rare in discrete heartbeats because of the limits of resolution of signals collection, and more importantly equal states contain underlying important cardiac regulation information which is neglected by the original permutative method and some measurements of time irreversibility .
After revision: Symbolic relative entropy, an efficient nonlinear complexity parameter measuring probabilistic divergences of symbolic sequences, is proposed in our nonlinear dynamics analysis of heart rates . Equal values are not rare in discrete heartbeats because of the limits of resolution of signals collection, and more importantly equal states contain underlying important cardiac regulation information which is neglected by the original permutative method and some measurements of time irreversibility .