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Integral fluctuation theorems and trace-preserving map.

Zhiqiang Huang1

  • 1Innovation Academy for Precision Measurement Science and Technology, <a href="https://ror.org/00zky9d41">Chinese Academy of Sciences</a>, Wuhan 430071, China.

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Summary
This summary is machine-generated.

This study reveals symmetry in entropy production probability generating functions, simplifying fluctuation theorems. A novel mapping approach integrates measurements and evolution, offering a new perspective on these fundamental principles.

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Area of Science:

  • Thermodynamics
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • The detailed fluctuation theorem highlights symmetry in entropy production probability generating functions.
  • Integral fluctuation theorems are derived from this symmetry and probability normalization.

Purpose of the Study:

  • To reformulate the generating function by incorporating measurements and system evolution.
  • To demonstrate a novel mapping approach for analyzing fluctuation theorems.
  • To explore the applicability of this method to related concepts like quasiprobability distributions.

Main Methods:

  • Constructing a completely positive mapping that integrates measurements and evolution.
  • Analyzing the trace-preserving property of these constructed maps.
  • Applying the method to the eigenstate fluctuation theorem and heat exchange scenarios.

Main Results:

  • The integral fluctuation theorem is shown to be a consequence of the trace-preserving property of the constructed maps.
  • The developed method provides a unified framework for understanding fluctuation theorems.
  • The Petz recovery map emerges naturally when applying the method to quasiprobability generating functions.

Conclusions:

  • The novel mapping approach offers a convenient and powerful tool for studying fluctuation theorems.
  • This framework extends to quasiprobability distributions, revealing connections to quantum information theory concepts.
  • The study provides new insights into the fundamental nature of entropy production and thermodynamics in driven systems.