A battery system in one embodiment includes a cell with an anode including graphite and a minor active material that displays an apparent thermodynamic hysteresis. A controller is operably connected to a memory which is configured to execute program instructions in the memory to perform a charge of the cell to a first potential, and a discharge of the cell from the first potential to generate a first discharge versus capacity curve. After a second charge of the cell to a second potential and a second discharge of the cell from the second potential to generate a second discharge versus capacity curve, the controller identifies a shift between the first discharge versus capacity curve and the second discharge versus capacity curve and updates a model of the cell based upon the identified shift. The controller then modifies at least one operating parameter of the cell based upon the updated model.