KL-Geometric Structure of Observer Entropy: A Minimal Information-Theoretic Framework

Key Points

• The central aim is to develop a framework for understanding observer entropy through the lens of information geometry.
• Defined observer entropy based on Kullback-Leibler divergence under coarse-graining.
• Established a finite information-geometric framework for observer entropy.
• Derived the Bridge Theorem demonstrating the local expansion of observer entropy.
• The main result shows observer entropy is influenced by the Fisher information matrix at leading order.
• Local expansion involves terms including Fisher information and higher-order corrections.
• An example of softmax and a resolution–information trade-off were discussed.