Intrinsic Information-Theoretic Models.

Area of Science:

• Mathematical Physics
• Information Geometry
• Quantum Physics Foundations

Background:

• Previous work established an information geometry framework for physical objects.
• This paper extends the framework by relaxing independence conditions for information sources.

Purpose of the Study:

• To develop a mathematical framework based on information geometry for representing physical objects.
• To lay informational foundations for physics, particularly quantum physics.
• To explore the implications of relaxed independence conditions on information modeling.

Main Methods:

• Modeling information sources using univariate and multivariate normal probability distributions.
• Applying concepts from information geometry and quantum mechanics (Schrödinger's equation).
• Utilizing the Mahalanobis distance and Cramér-Rao lower bound.

Main Results:

• Relaxed independence leads to modeling information as modes with a multivariate normal distribution.
• Information is decomposed into quantum harmonic oscillators, yielding intrinsic energy levels.
• The expectation of quadratic Mahalanobis distance equals quantum harmonic oscillator energy levels.
• The global probability density function matches Bayesian posterior distributions with a Riemannian volume prior.

Conclusions:

• The extended framework introduces complexity but yields invariant, intrinsic information-theoretic models.
• These intrinsic models are crucial for establishing foundational principles in physics.
• The study reinforces the connection between information geometry, quantum mechanics, and statistical inference.