Holographic entanglement of purification for thermofield double states and thermal quench

We explore the properties of holographic entanglement of purification (EoP) for two disjoint strips in the Schwarzschild-AdS black brane and the Vaidya-AdS black brane spacetimes. For two given strips separated by distance $D$ on the same boundary of Schwarzschild-AdS spacetime, the EoP decreases when we enlarge $D$ and turns to zero if $D$ is lager than a critical value. There is an upper bound for $D$, beyond which the EoP is always zero no matter how wide the strips are. In the case that two strips are in two boundaries of spacetime respectively, we find that the EoP decays exponentially with respective to time in certain time region. We also consider the EoP in the quench case and find that the EoP is only sensitive to the width of strips, while the holographic mutual information is sensitive not only to the width of strips but also the separation. Moreover, although the holographic mutual information changes continuously in the evolution process, the holographic EoP changes discontinuously.