The enstrophy (ω2/2) and passive scalar (ϕ) transport near the turbulent/non-turbulent (T/NT) interface is investigated using direct numerical simulation of a planar jet with passive scalar transport. To take into account the interface movement, we derive the transport equations for the enstrophy and the scalar in a local coordinate system moving with the T/NT interface. The characteristics of the T/NT interface are analyzed for three interface orientations. The cross-streamwise edge and the leading edge face the cross-streamwise and streamwise directions, respectively, and the trailing edge is opposite to the leading edge. The propagation velocity of the T/NT interface is derived from the enstrophy transport equation in the local coordinate system. The T/NT interface propagates toward the non-turbulent region on average at the cross-streamwise and leading edges, whereas the trailing edge frequently propagates into the turbulent region. The conditional average of the enstrophy transport equation in the local coordinate system shows that viscous diffusion transports, toward the non-turbulent region, enstrophy, that is advected from the turbulent core region or is produced slightly inside the T/NT interface. Viscous diffusion contributes greatly to the enstrophy growth in the region very close to the T/NT interface. The transport equation for the scalar ϕ in the local coordinate system is used to analyze the scalar transport near the T/NT interface. The conditional average of the advection term shows that ϕ in the non-turbulent region is frequently transported into the turbulent region across the cross-streamwise and leading edges by interface propagation toward the non-turbulent region. In contrast, ϕ in the turbulent region is frequently transported into the non-turbulent region across the trailing edge. The conditional averages of the advection and molecular diffusion terms show that both the interface propagation and the molecular diffusion contribute to the scalar transport across the T/NT interface.