  We derive the left-right entanglement entropy (LREE) for a bosonic
D$p$-brane. This brane has tangential dynamics and has been dressed by a $U(1)$
gauge potential, the Kalb-Ramond field and a tachyon field. For this purpose,
the R\'{e}nyi entropy will be computed and then, by taking a special limit of
it, the LREE will be obtained. Besides, the behavior of the LREE under the
tachyon condensation process will be evaluated. In addition, after the
transition of the system, i.e. the collapse of the unstable brane, the second
law of the thermodynamics on the LREE will be checked. We find that preserving
the second law imposes some conditions on the parameters of the setup.
