  Adopting the premise that the expected value of the quantum fluctuating
metric is linear, i.e., $\langle g^{\mu\nu}\rangle=\alpha g^{\mu\nu}$, we
analyze the modified gravity theory induced by the Einstein-Hilbert action
coupled to a matter field. This approach engenders the $f(R,T)$ gravity used to
investigate the braneworld. In this scenario, considering a thick brane, the
influence of metric fluctuations on brane dynamics is investigated.
Consequently, one shows how the metric fluctuations influence the vacuum
states. This influence has repercussions for modifying the brane energy and the
asymptotic profile of the matter field. After noticing these modifications, we
analyzed the most likely and stable structures from the matter field. One
performs this analysis considering the theoretical measure of differential
configurational entropy.
