  It has been shown by explicit and exact calculation that the geometric
product formula i.e. horizon area (or entropy) product formula of outer horizon
(${\cal H}^{+}$) and inner horizon (${\cal H}^{-}$) for charged accelerating
black hole (BH) should \emph{ neither be mass-independent nor it be quantized}.
This implies that the horizon area (or entropy ) product is mass-independent
conjecture has been~\emph{broken down} for charged accelerating BH. This also
further implies that the mass-independent feature of the area product of ${\cal
H}^{\pm}$ is \emph{not} a generic feature at all. We also compute that the
\emph{Cosmic-Censorship-Inequality} for this BH. Indeed it is violated for this
BH. Moreover, we compute the specific heat for this BH to determine the local
thermodynamic stability of this BH. Under certain criterion, the BH shows the
second order phase transition. Furthermore, we compute logarithmic corrections
to the entropy for the said BH due to small statistical fluctuations around the
thermal equilibrium.
