Entropic c-functions in $T\bar{T},J\bar{T},T\bar{J}$ deformations

We study the holographic entanglement entropy of an interval in a quantum field theory obtained by deforming a holographic two-dimensional conformal field theory via a general linear combination of irrelevant operators that are closely related to, but nonetheless distinct from, $T\bar{T},J\bar{T}$ and $T\bar{J}$, and compute the Casin-Huerta entropic $c$-function. We find that the entropic $c$-function is ultraviolet regulator independent, and along the renormalization group upflow towards the ultraviolet, it is non-decreasing. We show that the entropic $c$-function exhibits a power law divergence as the interval length approaches a minimum finite value determined in terms of the deformation parameters. We also find for a particular combination of the deformation parameters a square root correction of the entanglement entropy area law.