Glasses and gels, common amorphous solids with diverse applications, share intriguing similarities, including rigidity without translational order and dynamic slowing during ageing. However, their various underlying differences have not yet been explained. Here, through simulations, we elucidate distinct elastic properties related to temperature, observation times and ageing in glasses and gels, uncovering the underlying mechanisms. Configurational constraints, characterized by vibrational mean-squared displacements, similarly impact shear and bulk moduli in gels, but uniquely affect the shear modulus in glasses. As glasses age, a persistent trend of stiffening emerges, in contrast to gels, which initially stiffen and subsequently soften. We attribute these differences to mechanisms minimizing free energy: structural ordering in glasses and interface reduction in gels. Our findings not only reveal distinct behaviours but also shed light on the origin and evolution of elasticity in non-equilibrium disordered solids, with implications for amorphous material application and design.

玻璃和凝胶是具有多种应用的常见无定形固体，它们具有有趣的相似之处，包括没有平移顺序的刚性和老化过程中的动态减慢。然而，它们的各种根本差异尚未得到解释。在这里，通过模拟，我们阐明了玻璃和凝胶中与温度、观察时间和老化相关的不同弹性特性，揭示了潜在的机制。以振动均方位移为特征的构型约束类似地影响凝胶中的剪切模量和体积模量，但对玻璃中的剪切模量影响独特。随着眼镜老化，会出现持续的硬化趋势，而凝胶则相反，凝胶最初会变硬，随后会软化。我们将这些差异归因于最小化自由能的机制：玻璃中的结构排序和凝胶中的界面减少。我们的研究结果不仅揭示了独特的行为，而且还揭示了非平衡无序固体中弹性的起源和演化，对非晶材料的应用和设计具有重要意义。