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

We present a theoretical framework for a $\mathcal{P}\mathcal{T}$-symmetric double-cavity molecular optomechanical system demonstrating nonreciprocal enhancement of multipartite quantum entanglement at elevated temperatures. All bipartite entanglement channels ($E_{ac}$, $E_{a{B}_1}$, $E_{c{B}_2}$, $E_{B_1{B}_2}$) simultaneously maximize at optimal nonreciprocal asymmetry $J_1\mathrm{/}{J}_2\approx 5$, with entanglement persisting to $T\sim \text{SIrange}400500\text{kelvin}$ (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 (${\omega }_m\mathrm{/}2\pi =\text{SI}30\text{tera}\text{hertz}$), collective $\sqrt{N}$ coupling enhancement with $N=\text{num}e6$ 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 $\mathcal{P}\mathcal{T}$-symmetric architecture circumvents this fundamental trade-off, validated through rigorous stability analysis via Routh-Hurwitz criterion.