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Sub-Gaussian and subexponential fluctuation-response inequalities.

Yan Wang1

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This study introduces sub-Gaussian and subexponential distributions to analyze non-equilibrium systems. We establish bounds on physical quantities and entropy differences, generalizing the thermodynamic uncertainty relation for experimental applications.

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Area of Science:

  • Statistical mechanics
  • Non-equilibrium thermodynamics
  • Information theory

Background:

  • Sub-Gaussian and subexponential distributions are crucial for characterizing random phenomena.
  • The fluctuation-response relation is fundamental in understanding systems far from equilibrium.
  • Existing thermodynamic uncertainty relations often apply to specific equilibrium or near-equilibrium regimes.

Purpose of the Study:

  • To introduce and apply sub-Gaussian and subexponential distributions to non-equilibrium systems.
  • To establish theoretical bounds on physical quantities and entropy differences.
  • To generalize the thermodynamic uncertainty relation and address experimental applicability.

Main Methods:

  • Introduction and application of sub-Gaussian and subexponential distributions.
  • Derivation of bounds on expected value differences using sub-Gaussian/subexponential norms.
  • Generalization of fluctuation-response relations and thermodynamic uncertainty relations.
  • Analysis of experimental operational issues and non-asymptotic error bounds.

Main Results:

  • A bound is established for the difference in expected values of sub-Gaussian or subexponential quantities.
  • The entropy difference between two states is shown to be bounded by energy fluctuations.
  • Generalized thermodynamic uncertainty relations are derived for various regimes.
  • Non-asymptotic bounds on sample mean errors in fluctuation-response inequalities are provided.

Conclusions:

  • Sub-Gaussian and subexponential distributions offer a powerful framework for non-equilibrium statistical mechanics.
  • The derived bounds provide new insights into the relationship between entropy, energy fluctuations, and response.
  • The results offer practical guidelines for applying these theoretical findings in experimental settings.