INAEB (I'm not an expert, but...) Your battery discharged while e is high may discharge more energy (shiver at the thought), but can you actually do more with that energy? If that battery is in a flashlight it now has to work against a higher e value to emit photons, in the end you may well end up emitting the same number of photons with the same wavelength, resulting in the same net change in entropy as if you had used your batteries while e was still small.