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The differential capacitance comprises the most relevant thermodynamic information about an electrochemical system. Classical approaches to describe electrochemical capacitance have difficulties to combine the treatment of the ionic contribution of the electrolyte with the electronic contribution of the electrode. Moreover, different approaches are typically required for the description of the double-layer capacitance, on the one hand, and the pseudocapacitive contribution due to adsorption or intercalation of reactive species, on the other. In the present work, a new approach to describe electrochemical capacitance from first principles is developed. The treatment of a general electrochemical system at the level of multicomponent density-functional theory (MCDFT) yields an exact analytical expression for the total capacitance of the system, which corresponds to a formal series-circuit partitioning into "quantum" capacitance contributions of the density of states of electrons and ions, the (mean-field) electrostatic capacitance, as well as capacitance contributions of exchange and correlation among all active species. It is shown that the classical expression of the double-layer capacitance involving the interfacial Galvani potential is obtained in the limit of extended electrode and electrolyte regions. Importantly, the present formalism also describes systems with confined electrode and electrolyte phases, where the definition of the (classical) inner potentials of the electrode and electrolyte domains becomes problematic. Moreover, the new approach unifies the treatment of double-layer capacitance and pseudocapacitance resulting from reactive processes. [Display omitted] • Multicomponent DFT enables first-principles treatment of electrochemical capacitance. • Multicomponent Kohn–Sham equations yield exact expression for the total capacitance. • Capacitance includes contribution of density of states, electrostatics, correlation. • Classical capacitance corresponds to bulk limit of electrode and electrolyte phases. • New formalism includes description of pseudocapacitance due to reactive processes. [ABSTRACT FROM AUTHOR]