  The honeycomb lattice iridates $A_2$IrO$_3$ ($A =$ Na, Li) are candidates for
realization of the Kitaev-Heisenberg model although their proximity to Kitaev's
quantum Spin-Liquid (QSL) is still debated. We report on heat capacity $C$ and
entropy $S_{mag}$ for $A_2$IrO$_3$ ($A =$ Na, Li) in the temperature range
$0.075~{\rm K}\leq T \leq<EMAIL_ADDRESS>We find a well separated two-peak structure
for the magnetic heat capacity $C_{mag}$ for both materials and $S_{mag}$ for
Na$_2$IrO$_3$ shows a shoulder between the peaks with a value close to ${1\over
2}$Rln$2$. These features signal the fractionalization of spins into Majornana
Fermions close to Kitaev's QSL [Phys. Rev. B {\bf 92}, 115122 (2015); Phys.
Rev. B {\bf 93}, 174425 (2016).]. These results provide the first thermodynamic
evidence that $A_2$IrO$_3$ are situated close to the Kitaev QSL. Additionally
we measure the high temperature $T\leq 1000$~K magnetic susceptibility $\chi$
and estimate the Weiss temperature $\theta$ in the true paramagnetic state. We
find $\theta \approx -127$~K and $-105$~K, for Na$_2$IrO$_3$ and Li$_2$IrO$_3$,
respectively.
