  Gauge/gravity duality relates an AdS black hole with uniform boost with a
boosted strongly-coupled CFT at finite temperature. We study the perturbative
change in holographic entanglement entropy for strip sub-region in such gravity
solutions up to third order and try to formulate a first law of entanglement
thermodynamics including higher order corrections. The first law receives
important contribution from an entanglement chemical potential in presence of
boost. We find that suitable modifications to the entanglement temperature and
entanglement chemical potential are required to account for higher order
corrections. The results can be extended to non-conformal cases and AdS plane
wave background.
