Since its inception in the mid XIX century, statistical mechanics has aimed to understand the collective phenomena of many interacting elements. The first spectacular success was the derivation of the laws of perfect gases from the collisions of molecules. Until the 1970s, statistical mechanics studied the collective behavior of simple systems.
At that time, statistical mechanics studies discovered that even simple systems could have complex behavior, and this led to the development of the study of complex and disordered systems in physics, which then expanded to applications of all kinds. We are surrounded by complex systems and we ourselves are a complex system.
The importance of this field of research has been recognized in the motivations of the 2021 Nobel in Physics.
In the project Lotglassy we have studied several complex systems with the twofold aim of (i) extending our understanding of the detailed physical behavior of those made of simple elements and (ii) starting the study of those systems made of complex elements.
The project has concentrated mostly on the study of protypical complex systems, namely spin glasses and structural glasses at low temperature, hard spheres at high pressure, and other well-known disordered models, because the advancement in the comprehension of these models is crucial to develop more powerful theories.
However, many real-world applications are nowadays really complex systems whose study requires the same techniques developed in the Lotglassy project. A relevant example are the neural networks at the basis of the modern machine learning and artificial intelligence.
