  Maximum quantum work extraction is generally defined in terms of the
ergotropy functional, no matter how experimentally complicated is the
implementation of the optimal unitary allowing for it, especially in the case
of multipartite systems. In this framework, we consider a quantum battery made
up of many interacting sub-systems and study the maximum extractable work via
concurrent local unitary operations on each subsystem. We call the resulting
functional parallel ergotropy. Focusing on the bipartite case, we first observe
that parallel ergotropy outperforms work extraction via egoistic strategies, in
which the first agent A extracts locally on its part the maximum available work
and the second agent B, subsequently, extracts what is left on the other part.
For the agents, this showcases the need of cooperating for an overall benefit.
Secondly, from the informational point of view, we observe that the parallel
capacity of a state can detect entanglement and compare it with the statistical
entanglement witness that exploits fluctuations of stochastic work extraction.
Additionally, we face the technical problem of computing parallel ergotropy. We
derive analytical upper bounds for specific classes of states and Hamiltonians
and provide receipts to obtain numerical upper bounds via semi-definite
programming in the generic case. Finally, extending the concept of parallel
ergotropy, we demonstrate that system's free-time evolution and application of
local unitaries allow one to saturate the gap with the ergotropy of the whole
system.
