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We study the ground-state properties of a double layer graphene system with the Coulomb in terlayer 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 ther-modynamic 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 square (n), where the coeffcient 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 veried by current experiments.
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