  As the essential cause of the intrinsic dissipation that limits the quality
of graphene nanoresonators, intermodal energy transfer is also a key issue in
thermalization dynamics. Typically systems with larger initial energy demand
shorter time to be thermalized. However, we find quantitatively that instead of
becoming shorter, the equipartition time of the graphene nanoresonator can
increase abruptly by one order of magnitude. This thermalization frustration
emerges due to the partition of the normal modes based on the hierarchical
symmetry, and a sensitive on-off switching of the energy flow channels between
symmetry classes controlled by Mathieu instabilities. The results uncover the
decisive roles of symmetry in the thermalization at the nanoscale, and may also
lead to strategies for improving the performance of graphene nanoresonators.
