Upcoming experimental programs will look for signatures of a possible critical point in the QCD phase diagram in fluctuation observables. To understand and predict these signatures, one must account for the fact that the dynamics of any critical fluctuations must be out-of-equilibrium: because of critical slowing down, the fluctuations cannot stay in equilibrium as the droplet of QGP produced in a collision expands and cools. Furthermore, their out-of-equilibrium dynamics must also influence the hydrodynamic evolution of the cooling droplet. The recently developed Hydro+ formalism allows for a consistent description of both the hydrodynamics and the out-of-equilibrium fluctuations, including the feedback between them. We shall explicitly demonstrate how this works, setting up a Hydro+ simulation in a simplified setting: a rapidity-independent fireball undergoing radial flow with an equation of state in which we imagine a critical point close to the $\mu_B=0$ axis of the phase diagram. Within this setup, we show that we can quantitatively capture non-equilibrium phenomena, including critical fluctuations over a range of scales and memory effects. Furthermore, we illustrate the interplay between the dynamics of the fluctuations and the hydrodynamic flow of the fireball: as the fluid cools and flows, the dynamical fluctuations lag relative to how they would evolve if they stayed in equilibrium; there is then a backreaction on the flow itself due to the out-of-equilibrium fluctuations; and, in addition, the radial flow transports fluctuations outwards by advection. Within our model, we find that the backreaction from the out-of-equilibrium fluctuations does not yield dramatically large effects in the hydrodynamic variables. Further work will be needed in order to check this quantitative conclusion in other settings but, if it persists, this will considerably simplify future modelling.

中文翻译：

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了解 QCD 相图中临界点附近的失衡动力学

即将进行的实验程序将在波动可观测值的 QCD 相图中寻找可能临界点的特征。为了理解和预测这些特征，我们必须考虑这样一个事实，即任何临界波动的动力学都必须处于非平衡状态：由于临界减速，当碰撞中产生的 QGP 液滴膨胀时，波动不能保持平衡并冷却。此外，它们的失衡动力学也必须影响冷却液滴的流体动力学演化。最近开发的 Hydro+ 形式允许对流体动力学和非平衡波动的一致描述，包括它们之间的反馈。我们将明确演示这是如何工作的，在简化的设置中设置 Hydro+ 模拟：一个与速度无关的火球进行径向流动，具有状态方程，其中我们想象一个靠近相图 $\mu_B=0$ 轴的临界点。在此设置中，我们表明我们可以定量捕获非平衡现象，包括一系列尺度上的临界波动和记忆效应。此外，我们说明了波动动力学与火球流体动力学流动之间的相互作用：随着流体冷却和流动，动力学波动相对于它们保持平衡时的演化方式滞后；由于不平衡的波动，流动本身会发生逆反应；此外，径向流通过平流向外输送波动。在我们的模型中，我们发现来自失衡波动的反向反应不会对流体动力学变量产生显着的影响。为了在其他环境中检查这个定量结论，需要进一步的工作，但如果它持续存在，这将大大简化未来的建模。