Phenomena of disordered arrest represent a challenging and highly intriguing area of study in statistical physics. They are ubiquitous – ranging from the vitrification of viscoelastic fluids, polymers, and colloidal suspensions, to the jamming of granular materials in flow, and even to the kinetic arrest of epithelial tissues. Spanning disciplines from materials science and engineering to physics and biology, dynamic arrest remains a complex and poorly understood behavior. A key difficulty in characterizing these phenomena lies in the lack of a clear thermodynamic signature, such as a phase transition or critical point. As a result, kinetic arrest continues to be one of unsolved mysteries in the study of collective behavior in many-body systems, driving the need for new theoretical and analytical tools.

This is even more true today than before, since (due to a reorientation in the field towards biological, functional and programmable matter) the focus has shifted to strongly nonequilibrium systems. Already the glass transition itself implies – strictly speaking – a deviation from equilibrium, if one defines a glass as a fluid whose relaxation got stuck. But on top of that, colloidal suspensions under shear, synthetic actively driven matter mimicking the conversion of thermal energy into motion found in living systems, or such living systems themselves, are just a few examples of systems of interest that cannot be understood by equilibrium concepts.

This nonequilibrium nature and a microscopic approach to it are the key to understanding the generality among the widely different systems and the differences that appear upon closer examination. While equilibrium statistical physics is guided by the concept of universality and the related concept of coarse-grained theories, kinetic arrest phenomena such as the glass transition, the active glass transition, or the jamming transition appear alike at first, but they are not [1]. Loosely speaking, while equilibrium systems appear in equilibrium much the same way, every nonequilibrium system is out of equilibrium in its own way [2].

While the terms glass and jamming transition are used interchangeably in some context (especially in biology), they are in principle not. This highlights a key question to nonequilibrium statistical physics: can one provide a picture of the “generic yet not universal”?

This calls for theoretical frameworks that are rooted in the microscopic equations of motion with as little prior coarse-graining as possible. In the context of the glass transition, the mode-coupling theory of the glass transition (MCT) [3] is still one of the few fully microscopic and mathematically most advanced approaches. 42 years after its initial proposal, the main debates regarding MCT’s usefulness, successes and failures have settled, and the MCT-predicted cross-over point from fully fluidized to ideally arrested motion is regarded as a central point of reference. Also other theory frameworks, such as that of replica-symmetry breaking (RSB) connected to Nobel laureate Parisi, and the approaches to understand the glassy landscape of deep learning in neural networks (Nobel Prize 2024), in principle contain an MCT-like cross-over point.

MCT is at the center of recent developments in two directions: since its introduction in the context of colloidal rheology, the integration-through transients (ITT) formalism has been established as a generic framework to deal with statistical physics far from equilibrium [4]. Combined with MCT, it makes quantitative predictions for driven systems on a first-principles basis and allows performing in principle systematic coarse-graining to nonequilibrium transport coefficients [5]. Even more recently, some of the core issues with MCT have been reassessed in theories like the stochastic beta-relaxation theory (SBR) [6] or approaches using vertex renormalizations [7, 8]. Machine-learning and simulational tools have been further pushed to investigate the anatomy of kinetic arrest [9]. In combination, this provides us with novel theoretical tools to address the question: How to classify the different scenarios of kinetic arrest that appear in nonequilibrium systems across the disciplines?