  Using dual theories embedded into a larger unphysical Hilbert space along
entanglement cuts, we study the Entanglement Structure of $\mathbf{Z}_2$
lattice gauge theory in $(2+1)$ spacetime dimensions. We demonstrate Li and
Haldane's conjecture, and show consistency of the Entanglement Hamiltonian with
the Bisognano-Wichmann theorem. Studying non-equilibrium dynamics after a
quench, we provide an extensive description of thermalization in $\mathbf{Z}_2$
gauge theory which proceeds in a characteristic sequence: Maximization of the
Schmidt rank and spreading of level repulsion at early times, self-similar
evolution with scaling coefficients $\alpha = 0.8 \pm 0.2$ and $ \beta = 0.0
\pm 0.1$ at intermediate times, and finally thermal saturation of the von
Neumann entropy.
