Arthur Voter Los Alamos National Laboratory Theoretical Division I will discuss the characteristics and implementation of local hyperdynamics, which differs from standard hyperdynamics in that the biasing is performed locally, making it suitable for large systems. In standard hyperdynamics, the requirement that the bias potential be zero everywhere on the dividing surface bounding the current state has the consequence that for large systems the boost factor decays to unity, regardless of the form of the bias potential. In local hyperdynamics, the bias force on each atom is obtained by differentiating a local bias energy that depends only on the coordinates of atoms within a finite range D of this atom. This bias force is thus independent of the bias force in distant parts of the system, providing a method that gives a constant boost factor, independent of the system size. Although the resulting dynamics are no longer conservative, the method is surprisingly accurate. We have shown that local hyperdynamics should give correct results for a homogeneous system (all atoms equivalent), but it has been more difficult to explain why it remains extremely accurate for inhomogeneous systems as well. In this talk, I will present our best understanding of why the method works so well, and discuss our recent progress in implementing it in the LAMMPS code, allowing million-atom simulations on the millisecond time scale.