In some variations, an apparatus provides real-time monitoring of voltage and differential voltage of both anode and cathode in a battery configured with at least one reference electrode. Voltage monitors are connected to a computer programmed for receiving anode voltage signals; receiving cathode voltage signals; calculating the derivative of the anode voltage with respect to time or with respect to capacity; and calculating the derivative of the cathode voltage with respect to time or with respect to capacity. Other variations provide an apparatus for real-time assessment of capacities of both anode and cathode in a battery, comprising a computer programmed for receiving electrode voltage signals; estimating first and second electrode open-circuit voltages at two different times, and correlating the first and second electrode open-circuit voltages to first and second electrode states of charge, respectively, for each of anode and cathode. The anode and cathode capacities may then be estimated independently.