Before revision:  The relative entropy of modified permutation associated with equal states  shows advantages to these time irreversibility parameters and has great improvements to that of the original permutation. The temporal irreversibility researches on cardiac activities suggest the highest probabilistic asymmetry of the healthy young heart rates and highlight the facts that heart diseases and aging broke asymmetry, or reduce the nonlinear dynamical complexity , of human heartbeats .
After revision:  The relative entropy of modified permutation associated with equal states shows advantages to some nonlinear dynamics parameters without considering equalities. Researches on cardiac activities suggest the highest probabilistic asymmetry of the healthy young heart rates and highlight the facts that heart diseases and aging broke asymmetry, or reduce the nonlinear dynamical complexity , of human heartbeats .