  Devising a nonlinear extension of quantum mechanics is nontrivial because
unphysical features such as supraluminal communication (signaling) are to be
excluded. In this Letter, we show that the steepest entropy ascent formalism is
a viable no-signaling extension belonging to a broader class of no-signaling
nonlinear evolution equations for which the local evolution of a subsystem is
not necessarily bound to depend only on its reduced state. We prove that, in
addition to the local reduced density operator, there is a broad class of local
operators called `local perceptions', which are insensitive to unitary
operations localized within other non-interacting systems.
