  Protecting entanglement from decoherence is a critical aspect of quantum
information processsing. For many-body quantum systems evolving under
decoherence, estimating multipartite entanglement is challenging. This
challenge can be met up by considering distance based measure such as relative
entropy of entanglement which decisively measures entanglement in both pure as
well as mixed states. In this work, we investigate the tripartite entanglement
dynamics of pure and mixed states in the presence of a structured dephasing
environment at finite temperature. We show that the robustness of the quantum
system to decoherence is dependent on the distribution of entanglement and its
relation to different configurations of the bath. If the bath is structured
individually such that each qubit has its own environment, the system has
different dynamics compared to when the bath is common to all the three qubits.
From the results we conjecture that there is a connection between the
distribution of entanglement among the qubits and the distribution of bath
degrees of freedom, and the interplay of these two distributions determines the
decay rate of the entanglement dynamics. The sustainability of tripartite
entanglement is shown to be enhanced significantly in presence of reservoir
memory.
