  An equivalence between non equilibrium steady states (NESS) driven by a
time-independent force and stochastic pumps (SP) stirred by a time-varying
conservative force is studied for general many-body diffusive systems. When the
particle density and current of NESS are imitated by SP time-averaged
counterparts, we prove that the entropy production rate in NESS is always
greater than that of SP, provided that the conductivity of the particle current
is concave as a function of the particle density. Searching for a SP protocol
that saturates the entropy production bound reveals an unexpected connection
with traffic waves, where a high density region propagates against the
direction of the particle current.
