  The stress of a fluid on a confining wall is given by the mechanical wall
forces, independent of the nature of the fluid being passive or active. At
thermal equilibrium, an equation of state exists and stress is likewise
obtained from intrinsic bulk properties; even more, stress can be calculated
locally. Comparable local descriptions for active systems require a particular
consideration of active forces. Here, we derive expressions for the stress
exerted on a local volume of a systems of spherical active Brownian particles
(ABPs). Using the virial theorem, we obtain two identical stress expressions, a
stress due to momentum flux across a hypothetical plane, and a bulk stress
inside of the local volume. In the first case, we obtain an active contribution
to momentum transport in analogy to momentum transport in an underdamped
passive system, and we introduce an active momentum. In the second case, a
generally valid expression for the swim stress is derived. By simulations, we
demonstrate that the local bulk stress is identical to the wall stress of a
confined system for both, non-interacting ABPs as well as ABPs with
excluded-volume interactions. This underlines the existence of an equation of
state for a system of spherical ABPs. Most importantly, our calculations
demonstrated that active stress is not a wall (boundary) effect, but is caused
by momentum transport. We demonstrate that the derived stress expression
permits the calculation of the local stress in inhomogeneous systems of ABPs.
