The Fourier analysis of the final particle distribution followed by cumulant study of the Fourier coefficient event-by-event fluctuation is one of the main approaches for testing the collective evolution in the heavy-ion collision. Using a multidimensional generating function, we propose a method to extract any possible cumulant of multiharmonic flow fluctuations and classify them in terms of the order of cumulants and harmonics involved in them. In particular, we show that there are 33 distinct cumulants with order 2, 3, 4, 5 and harmonics 2, 3, 4, 5. We compute the normalized version of these cumulants from hydrodynamic simulation for Pb–Pb collisions based on T\(_\mathtt{R}\)ENTo+VISH2+1+UrQMD. We compare the simulation with those normalized cumulants that the LHC has measured and predict the unmeasured ones. Comparing the initial and final state fluctuation normalized cumulants, we compute the linear and nonlinear hydrodynamic response couplings. We finally introduce the genuine three-particle correlation function containing information of all third-order cumulants.

对最终粒子分布进行傅里叶分析，然后对傅里叶系数逐个事件波动进行累积研究，是测试重离子碰撞集体演化的主要方法之一。使用多维生成函数，我们提出了一种方法来提取多谐波流动波动的任何可能的累积量，并根据累积量和谐波的顺序对其进行分类。特别是，我们表明有 33 种不同的累积量，阶数为 2、3、4、5 和谐波 2、3、4、5。我们基于T \ (_\mathtt{R}\) ENTo + VISH2+1 + UrQMD. 我们将模拟与大型强子对撞机测量的那些归一化累积量进行比较，并预测未测量的累积量。比较初始和最终状态波动归一化累积量，我们计算线性和非线性流体动力响应耦合。我们最后介绍了包含所有三阶累积量信息的真正的三粒子相关函数。