  We consider the minimal area of the entanglement wedge cross section (EWCS)
in Einstein gravity. In the context of holography, it is proposed that this
quantity is dual to different information measures, e.g., entanglement of
purification, logarithmic negativity and reflected entropy. Motivated by these
proposals, we examine in detail the low and high temperature corrections to
this quantity and show that it obeys the area law even in the finite
temperature. We also study EWCS in nonrelativistic field theories with
nontrivial Lifshitz and hyperscaling violating exponents. The resultant EWCS is
an increasing function of the dynamical exponent due to the enhancement of
spatial correlations between subregions for larger values of $z$. We find that
EWCS is monotonically decreasing as the hyperscaling violating exponent
increases. We also obtain this quantity for an entangling region with singular
boundary in a three dimensional field theory and find a universal contribution
where the coefficient depends on the central charge. Finally, we verify that
for higher dimensional singular regions the corresponding EWCS obeys the area
law.
