LREE of an Unstable Dressed-Dynamical D$p$-brane: Superstring Calculations

We obtain the left-right entanglement entropy (LREE) for a D$p$-brane with tangential motion in the presence of a $U(1)$ gauge potential, the Kalb-Ramond field and an open string tachyon field. Thus, at first we extract the R\'{e}nyi entropy and then by taking a special limit of it we acquire the entanglement entropy. We shall investigate the behavior of the LREE under the tachyon condensation phenomenon. We observe that the deformation of the LREE, through this process, reveals the collapse of the brane. Besides, we examine the second law of thermodynamics for the LREE under tachyon condensation, and we extract the imposed constraints. Note that our calculations will be in the context of the type IIA/IIB superstring theories.