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Related Experiment Video

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Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

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Information flow and causality as rigorous notions ab initio.

¹Nanjing Institute of Meteorology, Nanjing 210044, China and China Institute for Advanced Study, Beijing 100081, China.

Physical Review. E

|December 15, 2016

Summary

This study rigorously derives information flow from first principles, establishing a theorem for nil causality. It quantizes information transfer in dynamical systems, analytically proving causation implies correlation, not vice-versa.

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Area of Science:

Physics
Dynamical Systems Theory
Information Theory

Background:

Information flow is a fundamental concept in physics, often treated axiomatically.
Existing methods like transfer entropy and Granger causality tests have limitations in verifying nil causality.
The relationship between causality and correlation remains a long-standing philosophical and scientific debate.

Purpose of the Study:

To rigorously derive the concept of information flow from first principles.
To establish the principle of nil causality as a proven theorem within dynamical systems.
To analytically investigate information flow in various deterministic and stochastic dynamical systems.

Main Methods:

Derivation of information flow from fundamental physical principles.
Development of a closed-form expression for information flow.
Application and testing of the derived formulas on benchmark dynamical systems (e.g., Kaplan-Yorke map, Rössler system).

Main Results:

Information flow is rigorously derived, not merely proposed as an ansatz.
The principle of nil causality is proven as a theorem, overcoming limitations of existing tests.
Explicit closed-form solutions for information flow were obtained for discrete and continuous time systems.
Analysis of benchmark systems revealed expected causal relations and tractable information flow structures.
For linear systems, it was analytically shown that causation implies correlation, but correlation does not imply causation.

Conclusions:

Information flow can be rigorously derived from first principles, with deep ties to causality in dynamical systems.
The study provides a theoretical framework and practical tools for quantifying information transfer in complex systems.
The findings offer a mathematical resolution to the philosophical debate on causation versus correlation.