  We study the evolution of the configuration entropy for different
combinations of $\Omega_{m0}$ and $\Omega_{\Lambda0}$ in the flat $\Lambda$CDM
universe and find that the cosmological constant plays a decisive role in
controlling the dissipation of the configuration entropy. The configuration
entropy dissipates at a slower rate in the models with higher value of
$\Omega_{\Lambda0}$. We find that the entropy rate decays to reach a minimum
and then increases with time. The minimum entropy rate occurs at an earlier
time for higher value of $\Omega_{\Lambda0}$. We identify a prominent peak in
the derivative of the entropy rate whose location closely coincides with the
scale factor corresponding to the transition from matter to $\Lambda$
domination. We find that the peak location is insensitive to the initial
conditions and only depends on the values of $\Omega_{m0}$ and
$\Omega_{\Lambda0}$. We propose that measuring the evolution of the
configuration entropy in the Universe and identifying the location of the peak
in its second derivative would provide a new and robust method to probe the
mass density and the cosmological constant.
