  The property that a Jacobi matrix is reflectionless is usually characterized
either in terms of Weyl m-functions or the vanishing of the real part of the
boundary values of the diagonal matrix elements of the resolvent. We introduce
a characterization in terms of stationary scattering theory (the vanishing of
the reflection coefficients) and prove that this characterization is equivalent
to the usual ones. We also show that the new characterization is equivalent to
the notion of being dynamically reflectionless, thus providing a short proof of
an important result of [Breuer-Ryckman-Simon]. The motivation for the new
characterization comes from recent studies of the non-equilibrium statistical
mechanics of the electronic black box model and we elaborate on this
connection. To appear in Commun. Math. Phys.
