  BaBar collaboration announced that they observed time reversal (T) asymmetry
through $B$ meson system. In the experiment, time dependencies of two
distinctive processes, $B_- \rightarrow \bar{B^0}$ and $\bar{B^0}\rightarrow
B_-$($-$ expresses CP value) are compared with each other. In our study, we
examine event number difference of these two processes. In contrast to the
BaBar asymmetry, the asymmetry of events number includes the overall
normalization difference for rates. Time dependence of the asymmetry is more
general and it includes terms absent in one used by BaBar collaboration. Both
of the BaBar asymmetry and ours are naively thought to be T-odd since two
processes compared are related with flipping time direction. We investigate the
time reversal transformation property of our asymmetry. Using our notation, one
can see that the asymmetry is not precisely a T-odd quantity, taking into
account indirect CP and CPT violation of K meson systems. The effect of
$\epsilon_K$ is extracted and gives rise to $\mathcal{O}(10^{-3})$
contribution. The introduced parameters are invariant under rephasing of quarks
so that the coefficients of our asymmetry are expressed as phase convention
independent quantities. Some combinations of the asymmetry enable us to extract
parameters for wrong sign decays of $B_d$ meson, CPT violation, etc. We also
study the reason why the T-even terms are allowed to contribute to the
asymmetry, and find that several conditions are needed for the asymmetry to be
a T-odd quantity.
