  Thermalization in nonlinear systems is a central concept in statistical
mechanics and has been extensively studied theoretically since the seminal work
of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling
of a ring-down setup, we show that thermalization due to nonlinear mode
coupling intrinsically limits the quality factor of nanomechanical graphene
drums and turns them into potential test beds for FPU physics. We find the
thermalization rate $\Gamma$ to be independent of radius and scaling as
$\Gamma\sim T^*/\epsilon_{{\rm pre}}^2$, where $T^*$ and $\epsilon_{{\rm pre}}$
are effective resonator temperature and prestrain.
