  A generic theory of the quasi-particle superconducting gap in underdoped
cuprates is derived in the strong coupling limit, and found to describe
extremely well the experimental "second gap" in \textit{absolute scale}. In
drastic contrast to the standard theories of Bogoliubov quasi-particle
excitations, the quasi-particle gap is shown to originate from anomalous
kinetic process, completely unrelated to the pairing strength. Furthermore, the
$k$-dependence of the gap deviates significantly from the pure
$d_{x^2-y^2}$-wave of the order parameter. Our study reveals a new paradigm for
the nature of superconducting gap, and is expected to reconcile numerous
apparent contradictions among existing experiments toward a more coherent
understanding of high-temperature superconductivity.
