  The organic system,
$\kappa$-[(BEDT-TTF)$_{1-x}$(BEDT-STF)$_x$]$_2$Cu$_2$(CN)$_3$, showing the Mott
transition between a nonmagnetic Mott insulating (NMI) state and a Fermi liquid
(FL), is systematically studied by calorimetric measurements. An increase of
the electronic heat capacity at the transition from the NMI state to the FL
state which keeps the triangular dimer lattice demonstrates that the charge
sector lost in the Mott insulating state is recovered in the FL state. We
observed that the remaining low-energy spin excitations in the Mott insulating
state show unique temperature dependence, and that the NMI state has a larger
lattice entropy originating from the frustrated lattice, which leads to the
Pomeranchuk-like effect on the electron localization. Near the Mott boundary,
an unexpected enhancement and magnetic-field dependence of heat capacity are
observed. This anomalous heat capacity is different from the behavior in the
typical first-order Mott transition and shows similarities with quantum
critical behavior. To reconcile our results with previously reported scenarios
about a spin gap and the first-order Mott transition, further studies are
desired.
