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Summary
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This study establishes a quantitative link between Shannon entropy and entropy production in stochastic thermodynamics. It reveals a fundamental trade-off between decision accuracy and entropy production in decision-making models.

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Area of Science:

  • Stochastic Thermodynamics
  • Information Theory
  • Statistical Mechanics

Background:

  • Thermodynamic uncertainty relations link observable precision and entropy production.
  • Shannon entropy quantifies uncertainty in information theory.
  • A direct quantitative link between Shannon entropy and entropy production is lacking.

Purpose of the Study:

  • To establish a quantitative relationship between Shannon entropy of an observable and entropy production.
  • To introduce and utilize symmetry entropy to quantify observable distribution asymmetry.
  • To demonstrate a fundamental trade-off in stochastic decision-making.

Main Methods:

  • Formulation of an uncertainty relation using Shannon entropy and entropy production.
  • Introduction of symmetry entropy to measure distribution symmetry.
  • Application of the derived relation to the diffusion decision model.

Main Results:

  • Established a lower bound of ln2 for the sum of entropy production and symmetry entropy.
  • Proved that the sum of entropy production and Shannon entropy is no less than ln2.
  • Demonstrated a trade-off between decision accuracy and entropy production in the diffusion model.

Conclusions:

  • A fundamental uncertainty relation exists between Shannon entropy and entropy production.
  • Symmetry entropy provides a measure linked to entropy production.
  • The findings have implications for understanding stochastic decision-making processes.