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This study introduces information length, a mathematical tool to measure information change in stochastic processes. This metric quantifies disparities between probability density functions across systems.

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Area of Science:

  • Physics
  • Mathematics
  • Information Theory

Background:

  • Stochastic processes are fundamental across scientific disciplines.
  • System-specific variables often obscure universal principles.
  • A universal mathematical tool is needed to analyze diverse phenomena.

Purpose of the Study:

  • To develop a system-agnostic mathematical tool for analyzing stochastic processes.
  • To quantify the similarity and disparity between Probability Density Functions (PDFs).
  • To introduce and utilize information length (L(t)) for measuring information change.

Main Methods:

  • Utilizing information geometry to define a metric for comparing PDFs.
  • Defining information length L(t) for time-dependent PDFs.
  • Applying L(t) to analyze classical and quantum systems.

Main Results:

  • Information length L(t) quantifies information change uniquely for a given initial condition.
  • The metric successfully measures disparity between PDFs.
  • Demonstrated utility in understanding attractor structures.

Conclusions:

  • Information length provides a universal framework for analyzing stochastic processes.
  • This approach aids in understanding complex dynamics in both classical and quantum realms.
  • Information geometry offers powerful insights into fundamental scientific principles.