We address the question of reversibility of collective motions in the Kuramoto model with identical oscillators and global coupling. In such a system, the dynamics is constrained on a low-dimensional invariant submanifold. This submanifold is determined by the initial state of the system. The question can be roughly stated as follows: Supposed that we know the governing equations and the state of the system at a certain moment $T_1$, can we recover an initial state?

The answers to this question are exposed through simulations of the dynamics on two invariant submanifolds and comparison between them. We show that common noise induces non-reversible dynamics, however, depending on the initial state, this non-reversibility is sometimes invisible on the macroscopic level. In such a setup, reversibility appears as a geometric concept that is related to rotational symmetries in the system.

我们用相同的振荡器和全局耦合解决了仓本模型中集体运动的可逆性问题。在这样的系统中，动力学被限制在低维不变子流形上。该子流形由系统的初始状态决定。这个问题可以大致表述如下：假设我们知道某一时刻的控制方程和系统状态${Ť}_{\mathrm{1个}}$，我们可以恢复初始状态吗？

通过对两个不变子流形的动力学模拟以及它们之间的比较来揭示这个问题的答案。我们表明，普通噪声会引起不可逆的动力学，但是，根据初始状态，这种不可逆性有时在宏观上是看不见的。在这种设置中，可逆性表现为与系统中旋转对称性相关的几何概念。