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The "classical" thermodynamic and statistical mechanical theories of Gibbs and Boltzmann are both predicated on axiomatic assumptions whose applicability is hard to ascertain. Theoretical objections and an increasing number of observed deviations from these theories have led to sustained efforts to develop an improved mathematical and physical foundation for them, and the search for appropriate extensions that are generally applicable to condensed materials at low temperatures ( T ) and high material densities where the assumptions of these theories start to become particularly questionable. These theoretical efforts have largely focused on minimal models of condensed material systems, such as the Fermi-Ulam-Pasta-Tsingou model, and other simplified models of condensed materials that are amenable to numerical and analytic treatments and that can serve to illuminate essential features of relaxation processes in condensed materials under conditions approaching integrable dynamics where clear departures from classical thermodynamics and dynamics can be generally expected. These studies indicate an apparently general multi-step relaxation process, corresponding to an initial "fast" relaxation process (termed the fast β-relaxation in the context of cooled liquids), followed by a longer "equipartition time", namely, the α-relaxation time τ α in the context of cooled liquids. This relaxation timescale can be enormously longer than the fast β-relaxation time τ β so that τ α is the primary parameter governing the rate at which the material comes into equilibrium, and thus is a natural focus of theoretical attention. Since the dynamics of these simplified dynamical systems, originally intended as simplified models of real crystalline materials exhibiting anharmonic interactions, greatly resemble the observed relaxation dynamics of both heated crystals and cooled liquids, we adapt this dynamical system approach to the practical matter of estimating relaxation times in both cooled liquids and crystals at elevated temperatures, which we identify as weakly non-integrable dynamical systems.

We assess the validity of a range of models of glass formation based on molecular dynamics simulation results of the Kob-Andersen (KA) model system under a wide range of constant volume and constant pressure conditions. These models include the Adam-Gibbs model emphasizing configurational entropy, the string model emphasizing collective particle exchange motion, the shoving model emphasizing material elasticity, the localization model emphasizing dynamical free volume, and parabolic models based on the ideas of dynamic facilitation and, alternatively, the hypothesis that glass formation involves an avoided critical point. We demonstrate that these seemingly disparate models all provide a reasonable description of structural relaxation and diffusion data for the KA model system under all simulation conditions considered. Hence, the present study points to some unity in our understanding of the relationship between leading models of glass formation, supporting inferences drawn from previous studies of polymeric glass-forming liquids.

We systematically study glass formation in the well-known Kob-Andersen model over a wide range of densities and pressures as a basis for judging the "universality" of glass formation through a comparison to a recent systematic study of model polymeric glass-forming liquids. Our purpose is to establish general characteristics of glass formation, to identify new relations, and to discern which properties of glass-forming liquids are material-specific and which are "universal." To this end, we analyze a number of characteristic properties of glass formation, such as the structural relaxation time, self-diffusion coefficient, viscosity, characteristic temperatures, and fragility. We also consider a suite of properties presumably related to dynamic heterogeneity in an attempt to better understand its relation to structural relaxation. We demonstrate that the glassy dynamics in the Kob-Andersen model exhibit many of the essential trends observed in polymeric glass-forming liquids, pointing to a remarkable "universality" of many aspects of glass formation.