The collective flow of double-strangeness ${\mathrm{\Xi }}^{-}$ baryons and its sensitivity to the equation of state (EoS) of dense nuclear matter are investigated in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=4$–10 GeV using a pure hadronic transport model (AMPT-HC). By simulating semicentral collisions $(b=4–8.5 \mathrm{fm})$ with soft $(K_0=230 \mathrm{MeV})$ and stiff $(K_0=380 \mathrm{MeV})$ EoS parameterizations, we analyze the central evolution of compression density, ${\mathrm{\Xi }}^{-}$ production mechanisms, and collective flow observables. The results demonstrate that ${\mathrm{\Xi }}^{-}$ production, concentrated in the midrapidity region, exhibits stronger sensitivity to the EoS stiffness than single-strangeness hadrons, owing to its dependence on multistep strangeness-exchange processes in high-density regions. The directed flow $\left(v_1\right)$ and elliptic flow $\left(v_2\right)$ of ${\mathrm{\Xi }}^{-}$ further reveal distinctive EoS-driven dynamics: a stiff EoS generates stronger anisotropic pressure gradients during compression, leading to a pronounced $v_1$ slope at midrapidity and enhanced $v_2$ at high transverse momenta $(p_T>1.0\mathrm{GeV}/c)$. These observables, complementary in probing cumulative yields and intensive kinematics, highlight ${\mathrm{\Xi }}^{-}$ as a unique probe of the high-density EoS near the QCD phase boundary. The findings underscore the critical role of ${\mathrm{\Xi }}^{-}$ collective flow in constraining the nuclear matter EoS at suprasaturation densities.

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• Collective flow
• Equations of state of nuclear matter
• Heavy-ion reaction mechanisms
• Nuclear matter
• Nuclear reactions
• Particle & resonance production
• Relativistic heavy-ion collisions