  Thermal boundary conductance (TBC) is critical in many thermal and energy
applications. A decades-old puzzle has been that many of the measured TBCs,
such as those well characterized across Al/Si and ZnO/GaN interfaces,
significantly exceed theoretical results or even the absolute upper limit
called the ``radiation limit", suggesting the failure of the theory. Here, we
identify that for high-transmission interfaces, the commonly assumed phonon
local thermal equilibrium adjacent to the interface fails, and the measurable
phonon temperatures are not their emission temperature. We hence develop a
``nonequilibrium Landauer approach" and define the unique ``dressed" and
``intrinsic" TBCs. Combining our approach even with a simple diffuse mismatch
model (DMM) nearly doubles the theoretical TBCs across the Al/Si and ZnO/GaN
interfaces, and the theoretical results agree with experiments for the first
time. The radiation limit is also redefined and found to increase over 100\%
over the original radiation limit, and it can now well bound all the
experimental data.
