Understanding and classifying non-equilibrium many-body phenomena, analogously to the classification of equilibrium states of matter into universality classes^1,2, is an outstanding problem in physics. From stellar matter to financial markets, any many-body system can be out of equilibrium in a myriad of ways, and many are difficult to experiment on. It is therefore a major goal to establish universal principles that apply to different phenomena and physical systems. For equilibrium states, the universality seen in the self-similar spatial scaling of systems close to phase transitions lies at the heart of their classification. Recent theoretical work^{3,4,5,6,7,8,9,10,11,12,13,14} and experimental evidence^15,16 suggest that isolated many-body systems far from equilibrium generically exhibit dynamic (spatiotemporal) self-similar scaling, akin to turbulent cascades¹⁷ and the Family–Vicsek scaling in classical surface growth^18,19. Here we observe bidirectional dynamic scaling in an isolated quench-cooled atomic Bose gas; as the gas thermalizes and undergoes Bose–Einstein condensation, it shows self-similar net flows of particles towards the infrared (smaller momenta) and energy towards the ultraviolet (smaller length scales). For both infrared and ultraviolet dynamics we find that the scaling exponents are independent of the strength of the interparticle interactions that drive the thermalization.

理解和分类非平衡多体现象，类似于将物质的平衡状态分类为普遍性类别^1,2，是物理学中的一个突出问题。从恒星物质到金融市场，任何多体系统都可能以多种方式失去平衡，其中很多都难以进行实验。因此，建立适用于不同现象和物理系统的普遍原则是一个主要目标。对于平衡状态，在接近相变的系统的自相似空间尺度中看到的普遍性是其分类的核心。近期理论工作^{3,4,5,6,7,8,9,10,11,12,13,14}和实验证据^15,16表明远离平衡的孤立多体系统通常表现出动态（时空）自相似缩放，类似于湍流级联¹⁷和经典表面生长中的 Family-Vicsek 缩放^18,19。在这里，我们观察到孤立的骤冷冷却原子玻色气体中的双向动态缩放；随着气体热化并经历玻色-爱因斯坦凝聚，它显示出自相似的粒子流向红外线（更小的动量）和能量向紫外线（更小的长度尺度）。对于红外和紫外动力学，我们发现缩放指数与驱动热化的粒子间相互作用的强度无关。