Background: The near-equilibrium properties of a QCD plasma can be encoded into transport coefficients such as bulk and shear viscosity. In QCD, the ratio of these transport coefficients to entropy density, $\zeta/s$ and $\eta/s$, depends non-trivially on the plasma's temperature. Purpose: We show that in a 0+1D boost-invariant fluid, a temperature-dependent $\zeta/s(T)$ or $\eta/s(T)$ can be described by an equivalent effective viscosity $\left\langle \zeta/s \right\rangle_{\textrm{eff}}$ or $\left\langle \eta/s \right\rangle_{\textrm{eff}}$. We extend the concept of effective viscosity in systems with transverse expansion, and discuss how effective viscosities can be used to identify families of $\zeta/s(T)$ and $\eta/s(T)$ that lead to similar hydrodynamic evolution. Results: In 0+1D, the effective viscosity is expressed as a simple integral of $\zeta/s(T)$ or $\eta/s(T)$ over temperature, with a weight determined by the speed of sound of the fluid. The result is general for any equation of state with a moderate temperature dependence of the speed of sound, including the QCD equation of state. In 1+1D, a similar definition of effective viscosity is obtained in terms of characteristic trajectories in time and transverse direction. This leads to an infinite number of constraints on an infinite functional space for $\zeta/s(T)$ and $\eta/s(T)$. Conclusions: The definition of effective viscosity in a 0+1D system clarifies how infinite families of $\zeta/s(T)$ and $\eta/s(T)$ can result in nearly identical hydrodynamic temperature profiles. By extending the study to a boost-invariant cylindrical (1+1D) fluid, we identify an approximate but more general definition of effective viscosity that highlight the potential and limits of the concept of effective viscosity in fluids with limited symmetries.

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流体动力学膨胀的升压不变 QCD 等离子体中的有效粘度

背景：QCD 等离子体的近平衡特性可以编码为传输系数，例如体积和剪切粘度。在 QCD 中，这些传输系数与熵密度的比值 $\zeta/s$ 和 $\eta/s$ 非常依赖于等离子体的温度。目的：我们表明，在 0+1D 升压不变流体中，与温度相关的 $\zeta/s(T)$ 或 $\eta/s(T)$ 可以用等效的有效粘度 $\left\ 来描述langle \zeta/s \right\rangle_{\textrm{eff}}$ 或 $\left\langle \eta/s \right\rangle_{\textrm{eff}}$。我们扩展了横向膨胀系统中有效粘度的概念，并讨论了如何使用有效粘度来识别导致类似流体动力学演化的 $\zeta/s(T)$ 和 $\eta/s(T)$ 族. 结果：在 0+1D 中，有效粘度表示为 $\zeta/s(T)$ 或 $\eta/s(T)$ 对温度的简单积分，权重由流体的声速决定。结果对于任何具有中等声速温度依赖性的状态方程都是通用的，包括 QCD 状态方程。在 1+1D 中，有效粘度的类似定义是根据时间和横向的特征轨迹获得的。这导致 $\zeta/s(T)$ 和 $\eta/s(T)$ 对无限函数空间的无限数量约束。结论：0+1D 系统中有效粘度的定义阐明了 $\zeta/s(T)$ 和 $\eta/s(T)$ 的无限族如何导致几乎相同的流体动力学温度曲线。通过将研究扩展到升压不变的圆柱形 (1+1D) 流体，