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Holographic Entanglement Negativity and Thermodynamics in Backreacted AdS Black Hole

We investigate holographic entanglement negativity (HEN) as a probe of mixed state quantum correlations in a deformed AdS black hole background with backreaction sourced by a string cloud. The bulk geometry is dual to a strongly coupled large-$N_c$ gauge theory at finite temperature, backreacted by a finite density of heavy static fundamental quarks. We analyze entanglement thermodynamics and establish a first law like relation in the small backreaction regime by identifying the deformed black hole at zero temperature as the natural ground state of the dual field theory. Using analytic expansions in the low and high temperature limits, we compute the HEN for adjacent, bipartite and disjoint subsystem configurations and examine its dependence on the backreaction parameter $ρ$. Our results reveal that at low temperature and high effective temperature, backreaction increases the HEN signaling enhancement of distillable quantum correlations. We further compare the behavior of HEN with holographic entanglement entropy (HEE) and mutual information (MI), demonstrating that entanglement negativity provides a sharper diagnostic of the competition between thermal and quantum correlations in holographic plasmas with matter backreaction.