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A Metric for the Entropic Purpose of a System
Michael C Parker1, Chris Jeynes2, Stuart D Walker1
1School of Computer Science and Electrical Engineering, University of Essex, Colchester CO4 3SQ, UK.
Entropy (Basel, Switzerland)
|February 26, 2025
Summary
Scientists developed a new metric, entropic purpose, to quantify information system goals impersonally. This principle links information creation to energy dissipation, applicable in AI and cybersecurity.
Area of Science:
- Thermodynamics
- Information Theory
- Complex Systems
Background:
- Traditionally, purpose in systems is viewed as subjective and outside scientific inquiry.
- Claude Shannon's work provided an impersonal measure for information, paving the way for similar objective metrics.
Purpose of the Study:
- To formally define an impersonal measure of 'entropic purpose' for information systems.
- To establish a 'Principle of Least (entropic) Purpose' for information-producing systems.
- To explore applications of entropic purpose in artificial intelligence and cybersecurity.
Main Methods:
- Utilizing the theoretical framework of Quantitative Geometrical Thermodynamics.
- Defining entropic purpose as a line integral of an entropic 'purposive' Lagrangian in hyperbolic space across the complex temporal plane.
- Analyzing the variational (Euler-Lagrange) behavior of the defined Lagrangian.
Main Results:
- The defined entropic purpose is formally derived and shown to have appropriate variational properties.
- Entropic purpose is approximately identified with the empirically measurable quantity of information created by a system.
- Landauer's principle is extended to information creation, indicating energy dissipation in purposive systems.
Conclusions:
- A scientific, impersonal measure of 'entropic purpose' has been established.
- This metric connects information creation with fundamental thermodynamic principles, including energy dissipation.
- Entropic purpose offers potential applications in assessing system 'aliveness' in AI and distinguishing humans from bots in cybersecurity.
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