  We establish sharp long time asymptotic behaviour for a family of entropies
to defective Fokker-Planck equations and show that, much like defective finite
dimensional ODEs, their decay rate is an exponential multiplied by a polynomial
in time. The novelty of our study lies in the amalgamation of spectral theory
and a quantitative non-symmetric hypercontractivity result, as opposed to the
usual approach of the entropy method.
