The shapes of cooperatively rearranging regions in glassy liquids change from being compact at low temperatures to fractal or "stringy" as the dynamical crossover temperature from activated to collisional transport is approached from below. We present a quantitative microscopic treatment of this change of morphology within the framework of the random first order transition theory of glasses. We predict a correlation of the ratio of the dynamical crossover temperature to the laboratory glass transition temperature, and the heat capacity discontinuity at the glass transition, ∆Cp. The predicted correlation agrees with experimental results for the 21 materials compiled by Novikov and Sokolov.Our increased ability to visualize and experimentally probe supercooled liquids on the nanometer length scale has explicitly revealed the presence of cooperatively rearranging regions 1,2,3,4,5,6,7,8,9,10 (CRR's). The cooperative rearrangement of groups of many molecules has long been thought to underlie the dramatic slowing of liquid dynamics upon cooling and could also explain the non-exponential time dependence of relaxation in glassy liquids. Activated transitions of regions of growing size were postulated in the venerable Adam-Gibbs argument for the glass transition 11 . To move, a region, in the AG view, must have a minimum of two distinct conformational states. Natural as this suggestion is, the sizes predicted from literally applying this notion are far too small to explain laboratory observations. The minimal AG cluster would have only two particles since the measured entropy per particle is of order 1k B at the glass transition.A distinct approach, the random first order transition (RFOT) theory of glasses, is based on a secure statistical mechanical formulation at the mean field level 12,13,14,15,16,17,18,19 but also goes beyond mean field theory to explain the non-exponential, non-Arrhenius dynamics of supercooled liquids through the existence of compact, dynamically reconfiguring regions ("entropic droplets") 20,21,22 whose predicted size is, in contrast to the Adam-Gibbs bound, very much consistent with what has been measured (125-200 molecules), using both scanning microscopy 1,8 and NMR techniques 7,9 , at temperatures near to T g .Computer simulations 3,23,24 and light microscopy studies of colloidal glasses 10 , however, have revealed dynamically reconfiguring regions that are not compact and contain fewer particles. Some investigators describe these regions as "fractal 6 " while others use the term "strings 3 " to characterize them. It has been suggested that such "stringy" excitations should be taken as the fundamental objects in the theory of glass transitions. As we will show, the fractal nature of the dynamically reconfiguring regions in the relatively high temperature regime probed in current computer simulations follows naturally from RFOT theory. To be precise, RFOT theory predicts the shape of the reconfiguring regions changes from compact to fractal as the system is heated from low temperatures, chara...

Dynamics near the surface of glasses is generally much faster than in the bulk. Neglecting static perturbations of structure at the surface, we use random first order transition (RFOT) theory to show the free energy barrier for activated motion near a free surface should be half that of the bulk at the same temperature. The increased mobility allows the surface layers to descend much further on the energy landscape than the bulk ordinarily does. The simplified RFOT calculation, however, predicts a limiting value for the configurational entropy a vapor deposited glass may reach as a function of deposition rate. We sketch how mode coupling effects extend the excess free surface mobility into the bulk so that the glass transition temperature is measurably perturbed at depths greater than the naive length scale of dynamic cooperativity.

Thermodynamics and kinetics are thought to be linked in glass transitions. The quantitative predictions of alpha-relaxation activation barriers provided by the theory of glasses based on random first-order transitions are compared with the experimental results for 44 substances. The agreement found between the predicted activation energies near T(g) and experiment is excellent. These predictions depend on the configurational heat capacity change on vitrification and the entropy of melting the crystal which are experimental inputs.

Nearly all glass forming liquids display secondary relaxations, dynamical modes seemingly distinct from the primary alpha relaxations. We show that accounting for driving force fluctuations and the diversity of reconfiguring shapes in the random first order transition theory yields a low free energy tail on the activation barrier distribution which shares many of the features ascribed to secondary relaxations. While primary relaxation takes place through activated events involving compact regions, secondary relaxation corresponding to the tail is governed by more ramified, string-like, or percolation-like clusters of particles. These secondary relaxations merge with the primary relaxation peak becoming dominant near the dynamical crossover temperature Tc, where they smooth the transition between continuous dynamics described by mode-coupling theory and activated events.

In recent years it has become widely accepted that a dynamical length scale ξα plays an important role in supercooled liquids near the glass transition. We examine the implications of the interplay between the growing ξα and the size of the crystal nucleus, ξM, which shrinks on cooling. We argue that at low temperatures where ξα > ξM a new crystallization mechanism emerges enabling rapid development of a large scale web of sparsely connected crystallinity. Though we predict this web percolates the system at too low a temperature to be easily seen in the laboratory, there are noticeable residual effects near the glass transition that can account for several previously observed unexplained phenomena of deeply supercooled liquids including Fischer clusters, and anomalous crystal growth near Tg.

Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics, and kinetics, and relate these emergent properties to the structure of the underlying landscape. This Perspective aims to describe these analogies with examples from recent applications, and suggest avenues for new interdisciplinary research.

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely. These are precisely the situations that correspond to rare event dynamics for which the graph transformation was introduced.

A set of benchmark systems is defined to compare different computational approaches for characterizing local minima, transition states, and pathways in atomic, molecular, and condensed matter systems. Comparisons between several commonly used methods are presented. The strengths and weaknesses are discussed, as well as implementation details that are important for achieving good performance. All of the benchmarks and methods are provided in an online database to make the implementation details available and the results reproducible. While this paper provides a snapshot of the benchmark results, the online framework is structured to be dynamic and incorporate new methods and codes as they are developed.