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Foundations of algorithmic thermodynamics.

Aram Ebtekar1, Marcus Hutter2

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Algorithmic entropy, a new measure of information content, applies universally, even far from equilibrium. It quantifies a system's work capacity from individual states, unlike traditional methods.

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Area of Science:

  • Theoretical Physics
  • Information Theory
  • Statistical Mechanics

Background:

  • Traditional entropy measures (Boltzmann, Gibbs-Shannon) rely on predefined macrovariables and ensembles.
  • These methods are limited in applicability, especially for systems far from thermodynamic equilibrium.
  • A universal measure of information content is needed for broader physical system analysis.

Purpose of the Study:

  • To introduce and explore Gács's coarse-grained algorithmic entropy as a universal measure of information content.
  • To demonstrate its applicability to systems arbitrarily far from equilibrium.
  • To derive algorithmic versions of fundamental thermodynamic principles.

Main Methods:

  • Leveraging universal computation to define algorithmic entropy.
  • Applying Markovian coarse graining to measure-preserving dynamical systems.
  • Proving fluctuation inequalities, including algorithmic counterparts to Jarzynski's equality and Landauer's principle.

Main Results:

  • Algorithmic entropy quantifies information content without prior assumptions on macrovariables or ensembles.
  • Demonstrated applicability to systems arbitrarily far from equilibrium.
  • Derived algorithmic fluctuation inequalities, including versions of Jarzynski's equality, Landauer's principle, and the second law of thermodynamics.

Conclusions:

  • Algorithmic entropy provides a more general framework for information content and thermodynamic properties.
  • It accurately determines a system's actual capacity to do work from an individual state.
  • This approach offers a powerful tool for analyzing complex systems beyond classical thermodynamic limits.