  How the transport properties of an extended system is affected by coupling to
active reservoirs is a significant, yet virtually unexplored question. Here we
address this issue in the context of energy transport between two active
reservoirs connected by a chain of harmonic oscillators. The couplings to the
reservoirs, which exert correlated stochastic forces on the boundary
oscillators, lead to fascinating behavior of the energy current and kinetic
temperature profile, which we compute exactly in the thermodynamic limit. We
show that the stationary active current (i) changes non-monotonically as the
activity of the reservoirs are changed, leading to a negative differential
conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some
finite value of the activity drive. For the example of a dichotomous active
force, we find the physical origin of the NDC using nonequilibrium response
formalism. It turns out that the kinetic temperature profile remains uniform at
the bulk, and can be expressed in a form similar to the thermally driven case.
We show that despite this apparent similarity, no effective thermal picture can
be consistently built in general. However, such a picture emerges in the small
activity limit, where many of the well-known results are recovered.

Statistical Mechanics;Soft Condensed Matter