  Long-range interacting systems such as nitrogen vacancy centers in diamond
and trapped ions serve as useful experimental setups to probe a range of
nonequilibrium many-body phenomena. In particular, via driving, various
effective Hamiltonians with physics potentially quite distinct from short-range
systems can be realized. In this Letter, we derive general bounds on the linear
response energy absorption rates of periodically driven systems of spins or
fermions with long-range interactions that are sign changing and fall off as
$1/r^\alpha$ with $\alpha > d/2$. We show that the disordered averaged energy
absorption rate at high temperature decays exponentially with the driving
frequency. This strongly suggests the presence of a prethermal plateau in which
dynamics is governed by an effective, static Hamiltonian for long times, and we
provide numerical evidence to support such a statement. Our results are
relevant for understanding timescales of both heating and hence new dynamical
regimes described by effective Hamiltonians in such long-range systems.
