In infinite dimensions, many-body systems of pairwise interacting particles provide exact analytical benchmarks for the features of amorphous materials, such as the stress–strain curve of glasses under quasistatic shear. Here, instead of global shear, we consider an alternative driving protocol, as recently introduced by Morse etal 2020 (arXiv:2009.07706), which consists of randomly assigning a constant local displacement on each particle, with a finite spatial correlation length. We show that, in the infinite-dimensional limit, the mean-field dynamics under such a random forcing are strictly equivalent to those under global shear, upon a simple rescaling of the accumulated strain. Moreover, the scaling factor is essentially given by the variance of the relative local displacements of interacting pairs of particles, which encodes the presence of a finite spatial correlation. In this framework, global shear is simply a special case of a much broader family of local forcing, which can be explored by tuning its spatial correlations. We discuss the specific implications for the quasistatic driving of glasses—initially prepared at a replica-symmetric equilibrium—and how the corresponding ‘stress–strain’-like curves and elastic moduli can be rescaled onto their quasistatic-shear counterparts. These results hint at a unifying framework for establishing rigorous analogies, at the mean-field level, between different driven disordered systems.

在无限维度中，成对相互作用粒子的多体系统为非晶材料的特征提供了精确的分析基准，例如准静态剪切下玻璃的应力 - 应变曲线。在这里，我们考虑替代的驱动协议，而不是全局剪切，正如 Morse等人最近介绍的那样2020 (arXiv:2009.07706)，它包括在每个粒子上随机分配一个恒定的局部位移，具有有限的空间相关长度。我们表明，在无限维极限下，在对累积应变进行简单重新缩放后，这种随机强迫下的平均场动力学与全局剪切下的平均场动力学严格等效。此外，比例因子基本上由相互作用的粒子对的相对局部位移的方差给出，它编码了有限空间相关性的存在。在这个框架中，全球剪切只是更广泛的局部强迫家族的一个特例，可以通过调整其空间相关性来探索。我们讨论了玻璃准静态驱动的具体含义——最初是在复制对称平衡下准备的——以及如何将相应的“应力应变”样曲线和弹性模量重新调整到准静态剪切对应物上。这些结果暗示了一个统一的框架，用于在不同驱动的无序系统之间在平均场水平上建立严格的类比。