| Abstract: | As most materials are cooled below their melting temperature, they crystalize from a microscopically disordered liquid into a microscopically ordered solid. Under certain conditions however (e.g., very fast cooling) crystallization can be avoided, and one may can reach a new state of matter, known as a glass. Glasses are solid (exhibiting mechanical rigidity), while having a disordered microscopic structure, as in a liquid. Among other characteristics, one of the defining features exhibited by glasses is a ‘separation of relaxation time-scales’. That is, the microscopic movement of the glass’s particles can be distinctively separated in two – a fast vibrational motion of the particles in place (as in a solid), and a much slower motion tied to a reconfiguration of the entire microscopic structure (as in a liquid). These two types of motion are distinct enough that one can attribute a different entropy to each, the vibrational entropy – ????, and the configurational entropy – ???????. The sum of these entropies is the total entropy of the glass, ????. While methods for calculating these entropies exist in the literature, they do not afford a direct understanding of these entropies without invoking any specific theory. In addition, some of these methods require the system reach equilibrium, or apply only to particulate systems.
In this work, we propose a new entropy calculation method, the Concatenated Information (CCI) method, based on ideas from information theory. Requiring no specific theory, and being general enough to apply to any system exhibition a separation of relaxation time-scales, either in or out of equilibrium, we believe this method has advantages over other, existing methods. We test this method on two different glassy systems, and show that it returns the expected results. |
