Fluctuations in stored work bound the charging power of quantum batteries

We investigate the connection between the charging power of a quantum battery and the fluctuations of the work stored in it. We show that in order to have a non-zero rate of change of the extractable work, the work fluctuations must be non-zero. This is presented in terms of an uncertainty relationship that bounds the speed of the charging process of any quantum system. Our findings also identify quantum coherence in the battery as a resource in the charging process, which we illustrate on a toy model of a heat engine.