Data Science is a multidisciplinary field that plays a crucial role in
extracting valuable insights and knowledge from large and intricate datasets.
Within the realm of Data Science, two fundamental components are Information
Theory (IT) and Statistical Mechanics (SM), which provide a theoretical
framework for understanding dataset properties. IT enables efficient storage
and transmission of information, while SM focuses on the behavior of systems
comprising numerous interacting components. In the context of data science, SM
allows us to model complex interactions among variables within a dataset. By
leveraging these tools, data scientists can gain a profound understanding of
data properties, leading to the development of advanced models and algorithms
for analysis and interpretation. Consequently, data science has the potential
to drive accurate predictions and enhance decision-making across various
domains, including finance, marketing, healthcare, and scientific research.
In this paper, we apply this data science framework to a large and intricate
quantum mechanical system composed of particles. Our research demonstrates that
the dynamic and probabilistic nature of such systems can be effectively
addressed using a Multiscale Entropic Dynamics (MED) approach, derived from the
Boltzmann methods of SM. Through the MED approach, we can describe the system's
dynamics by formulating a general form of the Nonlinear Schr\"odinger equation
and how it can be applied to various systems with particles and
quasi-particles, such as electrons, plasmons, polarons, and solitons. By
employing this innovative approach, we pave the way for a deeper understanding
of quantum mechanical systems and their behaviors within complex materials.Comment: 12 page