  This paper analyzes general spatially-coupled (SC) systems with
multi-dimensional coupling. A continuum approximation is used to derive
potential functions that characterize the performance of the SC systems. For
any dimension of coupling, it is shown that, if the boundary of the SC systems
is fixed to the unique stable solution that minimizes the potential over all
stationary solutions, the systems can approach the optimal performance as the
number of coupled systems tends to infinity.
