Loops, Loop Sequences and Loop Surfaces in Statistical Geodesics, and Quantum Information

TL;DR

This paper investigates the geometric structures of probability flows in quantum information, focusing on loops, loop sequences, and surfaces in statistical geodesics, with implications across physics, mathematics, and information theory.

Contribution

It introduces the concept of loops, loop sequences, and surfaces in the geometry of probability spaces, linking them to physical and informational phenomena.

Findings

Loops and surfaces represent probability flow in quantum systems.

Geometric structures relate to entropy, gravity, and information theory.

Potential applications in physics and mathematics.

Abstract

The locus of probability flow in Quantum Mechanics and information is explored. We explore loops, loop sequences and loop surfaces in the statistical geodesics. Having known about the loop character of the statistical geodesics in probability space, we discuss wider physical aspects of consequences of the geometry of the probabilities in the form of loop sequences and loop surfaces. These are interpreted as the locus of probability flow. A deeper philosophical observation reveals that these loops, loop sequences and loop surfaces are the information grids. These investigations in many ways could be significant not only in the research in Statistics, but also in Mathematics, and Physics in general, and entropy, gravity and information theory in specific.