# Holographic first law of entanglement entropy ## Introduction - $\delta S_{B}=\delta\left\langle H_{B}\right\rangle$, i.e., variation of entanglement entropy equals variation of modular energy ## Renormalisation issues - RHS is by construction finite, but LHS is finite only if restricted to certain variations that avoid UV divergences ([[2013#Faulkner, Guica, Hartman, Myers, van Raamsdonk]]) - but [[2016#Taylor, Woodhead]] proposes a renormalisation method for [[0145 Generalised area]], and in [[2021#Taylor, Too]] they show that the renormalised HEE automatically satisfies the first law