Electrochemical reaction fuel cell system, comprising: a cathode (8), an anode (1), one at least of the anode and of the cathode comprising at least one metal, one metal hydroxide or one metal oxide in the molten state, a solid electrolyte (7), placed between the cathode and the anode, at least one regenerator (4) for regenerating, starting from one at least of the oxidation-reduction reaction products which is recovered at at least one of the anode and of the cathode, by a reaction, at least one of the products constituting at least one of the anode or of the cathode or the fuel or oxidizer consumed at at least one of the anode or of the cathode, one of the regeneration products being reintroduced into the system as electrode made of liquid metal or liquid metal oxide or in the form of fuel or oxidizer, one of the reactions making possible said regeneration or making possible the regeneration of one of the reactants of the oxidation-reduction reaction being endothermic.

A carbon-oxygen battery system, including a Boudouard reactor in fluid communication with an electrochemical cell; a carbon store configured to store carbon; a gas store in fluid communication with the electrochemical cell, and a fuel gauge. The gas store is configured to separately store oxygen and a carbon-containing gas, wherein the gas store comprises a movable barrier separating the oxygen from the carbon-containing gas. The fuel gauge configured to determine a state of charge based on a position of the movable barrier, a mass of the oxygen in the gas store, a mass of the carbon-containing gas in the gas store, a mass of carbon in the carbon store, a volume of carbon in the carbon store, or a combination thereof. The gas store and the electrochemical cell form a closed system.