  The Glauber-Exclusion process is a superposition of a Glauber dynamics and
the Symmetric Simple Exclusion Process (SSEP) on the lattice. The model was
shown to admit a reaction-diffusion equation as the hydrodynamic limit. In this
article, we define a notion of temperature regimes via the reaction function in
the equation and prove cutoff in the full high-temperature regime for the
attractive model in dimensions $1$ and $2$ with periodic boundary condition.
Our results show that the equation in the hydrodynamic limit reflects the
mixing behavior of the large but finite system. Besides, cutoff is proved under
the lack of reversibility and an explicit formula for the invariant measure. We
also provide the spectral gap and prove pre-cutoff in all dimensions. Our proof
involves a new interpretation of attractiveness, the information percolation
framework introduced by Lubetzky and Sly, anti-concentration of simple random
walk on the lattice, and a coupling inspired by excursion theory. We hope that
this approach can find new applications in the future.
