  We consider the dissipative charging process of quantum batteries in terms of
a collisional model, where the batteries are coupled to a heat bath using
non-energy preserving interactions. First, we show that for low temperatures
the collective process can attain a charging power that increases polynomically
with the number of batteries. The scaling we find is $N^3$ that, while being
grater than the bound obtained for unitary processes, it has a lower
efficiency. Then, we study the dissipative charging process of single battery
using a time dependent Hamiltonian that generates coherences in the energy
basis. In this case we find that the presence of coherence could enhance the
charging power and also its efficiency. Finally, we show how this process can
be used in a quantum heat engine that contains the charging process as one of
its open strokes.

Quantum Physics