  Motivated by exploring the thermalization process in relativistic and
non-relativistic holographic field theories after a non-local quench, we
investigate some features in the time evolution of the entanglement wedge cross
section (EWCS). This quantity is a possible holographic dual to some non-local
information measures such as entanglement of purification. In particular, we
focus on the time dependence of EWCS during black hole formation in D+2
dimensional AdS spacetime as well as geometries with Lifshitz and hyperscaling
violating exponents. A combination of analytic and numerical results for large
symmetric strip shaped boundary subregions shows that the scaling of EWCS at
early times only depends on the Lifshitz exponent. In addition, this early
growth regime is followed by a linear growth regime whose velocity depends on
the dimensions of spacetime, the Lifshitz exponent, and the hyperscaling
parameter. This velocity is the same as the entanglement velocity and for
nontrivial dynamical exponent depends on the temperature of the final
equilibrium state.
