  The exceptional properties of the two-dimensional material graphene make it
attractive for multiple functional applications, whose large-area samples are
typically polycrystalline. Here, we study the mechanical properties of graphene
in computer simulations and connect these to the experimentally relevant
mechanical properties. In particular, we study the fluctuations in the lateral
dimensions of the periodic simulation cell. We show that over short time
scales, both the area A and the aspect ratio B of the rectangular periodic box
show diffusive behavior under zero external field during dynamical evolution,
with diffusion coefficients DA and DB that are related to each other. At longer
times, fluctuations in A are bounded, while those in B are not. This makes the
direct determination of DB much more accurate, from which DA can then be
derived indirectly. We then show that the dynamic behavior of polycrystalline
graphene under external forces can also be derived from DA and DB via the
Nernst-Einstein relation. Additionally, we study how the diffusion coefficients
depend on structural properties of the polycrystalline graphene, in particular,
the density of defects.
