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Multipartite quantum entanglement in $\mathcal{PT}$-symmetric molecular optomechanics: Nonreciprocal enhancement and thermal resilience to \SI{500}{\kelvin}

We present a theoretical framework for a $\mathcal{PT}$-symmetric double-cavity molecular optomechanical system demonstrating nonreciprocal enhancement of multipartite quantum entanglement at elevated temperatures. All bipartite entanglement channels ($E_{ac}$, $E_{aB_1}$, $E_{cB_2}$, $E_{B_1B_2}$) simultaneously maximize at optimal nonreciprocal asymmetry $J_1/J_2 \approx 5$, with entanglement persisting to $T \sim \SIrange{400}{500}{\kelvin}$ (material-limited ceiling) two orders of magnitude beyond conventional optomechanical systems. This thermal resilience and balanced enhancement across all channels arise from synergistic combination of ultra-high-frequency molecular vibrations ($ω_m/2π= \SI{30}{\tera\hertz}$), collective $\sqrt{N}$ coupling enhancement with $N=\num{e6}$ molecules, and directional nonreciprocal coupling shielding entanglement-generating interactions from backaction noise. Unlike optical parametric amplifier schemes where vibration-vibration enhancement suppresses optical-vibration correlations, our $\mathcal{PT}$-symmetric architecture circumvents this fundamental trade-off, validated through rigorous stability analysis via Routh-Hurwitz criterion.