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On the Differential and the Integral Value of Information.

Raphael D Levine1,2,3

  • 1Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.

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|January 24, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces quantitative measures for the value of information, exploring both local and global perspectives within information theory and maximal entropy frameworks. These measures help analyze how information value changes with new data or over time.

Keywords:
Lagrange multiplierconstraints on a probability distributioncross correlation of constraintsmutual information

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Area of Science:

  • Information Theory
  • Statistical Mechanics
  • Quantitative Science

Background:

  • The value of information is crucial in decision-making and system analysis.
  • Existing frameworks often lack precise quantitative measures for information's value.
  • Maximal entropy principles offer a foundation for quantifying information.

Purpose of the Study:

  • To develop quantitative expressions for the value of information.
  • To explore both differential (local) and integral (global) measures.
  • To analyze how information value changes with additional input or parameters.

Main Methods:

  • Utilizing information theory and maximal entropy formulations.
  • Defining a local, differential measure for information value.
  • Defining a global, integral measure for information value.

Main Results:

  • A differential measure, akin to a potential with physical dimensions, was established.
  • An integral measure, possessing the dimension of information, was defined.
  • The differential measure allows analysis of information value dynamics over time or parameters.

Conclusions:

  • The study provides novel quantitative tools for assessing information value.
  • The developed measures offer insights into the changing value of information.
  • These quantitative expressions have potential applications in various fields analyzing information dynamics.