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Thermalization in nonlinear systems is a central concept in statisticalmechanics and has been extensively studied theoretically since the seminal workof Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modelingof a ring-down setup, we show that thermalization due to nonlinear modecoupling intrinsically limits the quality factor of nanomechanical graphenedrums and turns them into potential test beds for FPU physics. We find thethermalization 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.

FPU physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling