  We study the evolution of the configuration entropy of HI distribution in the
post-reionization era assuming different time evolution of HI bias. We describe
time evolution of linear bias of HI distribution using a simple form
$b(a)=b_{0} a^{n}$ with different index $n$. The derivative of the
configuration entropy rate is known to exhibit a peak at the scale factor
corresponding to the $\Lambda$-matter equality in the unbiased $\Lambda$CDM
model. We show that in the $\Lambda$CDM model with time-dependent linear bias,
the peak shifts to smaller scale factors for negative values of $n$. This is
related to the fact that the growth of structures in the HI density field can
significantly slow down even before the onset of $\Lambda$ domination in
presence of a strong time evolution of the HI bias. We find that the shift is
linearly related to the index $n$. We obtain the best fit relation between
these two parameters and propose that identifying the location of this peak
from observations would allow us to constrain the time evolution of HI bias
within the framework of the $\Lambda$CDM model.
