![]() ![]() Kob, Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics ( World Scientific, 2011). Dyre, “ Colloquium: The glass transition and elastic models of glass-forming liquids,” Rev. Cavagna, “ Supercooled liquids for pedestrians,” Phys. Stillinger, “ Supercooled liquids and the glass transition,” Nature 410, 259 (2001). ![]() Nagel, “ Supercooled liquids and glasses,” J. Biroli, “ Theoretical perspective on the glass transition and amorphous materials,” Rev. It is not our goal to review it, and we refer instead to previous articles. The rich phenomenology characterizing the approach to the glass transition has given rise to thick literature. The experimental glass transition is not a genuine phase transition, as it is not defined independently of the observer. Clearly, T g depends on the measurement time scale and shifts to lower temperatures for longer observation times. The liquid is then trapped virtually forever in one of many possible structurally disordered states: this is the basic phenomenology of the glass transition. In the latter case, the liquid remains structurally disordered, but its relaxation time increases so quickly that there exists a temperature, called the glass temperature T g, below which structural relaxation takes such a long time that it becomes impossible to observe. When a liquid is cooled, it can either form a crystal or avoid crystallization and become a supercooled liquid. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems. We describe a panel of available computational tools, offering for each method a critical discussion. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraught with difficulties, misconceptions, and paradoxes, and its physical relevance is vividly debated. The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition.
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