The possibility of using quantum effects to speed up the charging processes
of batteries have been vastly investigated. In order to traslate these ideas
into working devices it is however crucial to assess the stability of the
storage phase in the quantum battery elements when they are in contact with
environmental noise. In this work we formalize this problem introducing a
series of operationally well defined figures of merit (the work capacitances
and the Maximal Asymptotic Work/Energy Ratios) which gauge the highest
efficiency one can attain in recovering useful energy from quantum battery
models that are formed by large collections of identical and independent
elements (quantum cells or q-cells). Explicit evaluations of such quantities
are presented for the case where the energy storing system undergoes through
dephasing and depolarizing noise.Comment: 15 pages, 5 figure