  We study the ground-state properties of a double layer graphene system with
the Coulomb interlayer electron-electron interaction modeled within the random
phase approximation. We first obtain an expression of the quantum capacitance
of a two layer system. In addition, we calculate the many-body
exchange-correlation energy and quantum capacitance of the hybrid double layer
graphene system at zero-temperature. We show an enhancement of the majority
density layer thermodynamic density-of-states owing to an increasing interlayer
interaction between two layers near the Dirac point. The quantum capacitance
near the neutrality point behaves like square root of the total density,
$\alpha \sqrt{n}$, where the coefficient $\alpha$ decreases by increasing the
charge density imbalance between two layers. Furthermore, we show that the
quantum capacitance changes linearly by the gate voltage. Our results can be
verified by current experiments.
