I believe the first manuscript from the same authors (also on EES) gives some hints on the second one. in fact, the same authors even reported a spontaneous cell voltage increase in a symmetric Cu/glass electrolyte/Cu cell, formally in open circuit conditions. That is, creation of energy.
The authors stated that upon galvanostatic polarization of the symmetric copper cell Na metal is plated at the positive cell terminal (cathode). Difficult to believe. Most likely Na metal is plated at the negative cell terminal while the electrolyte is decomposed at the positive cell terminal (cathode).
Following the polarization, the cell was left in OC but still connected to the potentiostat-galvanostat. After some voltage up-and-down, the cell voltage increased “spontaneously” to 8 V. Clearly, the electronics of the equipment was was not really capable of ensuring open circuit conditions. This kind of mistakes are frequently made by fresh students fully trusting equipment.
Another point the authors did not consider in their work is the well known copper dissolution occurring at voltage above 2–2.5 (vs Li). This is actually the major problem associated with the overdischarge of Li-ion batteries and it is well known to Li battery scientists.