We unveil a quantum Pontus–Mpemba effect enabled by the Liouvillian skin effect in a
dissipative tight-binding chain with asymmetric incoherent hopping and coherent
boundary coupling. The skin effect, induced by non-reciprocal dissipation, localizes
relaxation modes near the system boundaries and gives rise to non-orthogonal spectral
geometry. While such non-normality is often linked to slow relaxation, we show that it can
instead accelerate relaxation through a two-step protocol – realizing a quantum
Pontus–Mpemba effect. Specifically, we consider a one-dimensional open chain with
coherent hopping J, asymmetric incoherent hoppings JR ̸= JL, and a controllable
end-to-end coupling ϵ. For ϵ = 0, the system exhibits the Liouvillian skin effect, with left
and right eigenmodes localized at opposite edges. We compare two relaxation protocols
toward the same stationary state: (i) a direct relaxation with ϵ = 0, and (ii) a two-step
(Pontus) protocol where a brief coherent evolution transfers the excitation across the
lattice before relaxation. Although both share the same asymptotic decay rate, the
two-step protocol relaxes significantly faster due to its reduced overlap with the slow
boundary-localized Liouvillian mode. The effect disappears when JR = JL, i.e., when the
skin effect vanishes. Our results reveal a clear connection between boundary-induced
non-normality and protocol-dependent relaxation acceleration, suggesting new routes for
controlling dissipation and transient dynamics in open quantum systems.