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Claudio A Cerdeiriña1, Jacobo Troncoso1

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This study introduces a new statistical ensemble for open thermodynamic systems, linking fluctuations in properties to measurable responses. This framework precisely quantifies thermodynamic behavior and validates with a water-like model.

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Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Physical Chemistry

Background:

  • Macroscopic systems exchange heat, work, and matter with surroundings.
  • Thermodynamic response functions characterize system behavior.
  • Understanding fluctuations is key to macroscopic properties.

Purpose of the Study:

  • Develop a statistical ensemble for completely open macroscopic systems.
  • Connect variances and covariances of extensive properties to thermodynamic response functions.
  • Generalize existing ensemble theories.

Main Methods:

  • Derivation of exact formulas for variances and covariances.
  • Analysis of ratios between extensive properties.
  • Application to a water-like Ising model for numerical validation.

Main Results:

  • Response functions quantify variances and covariances of property ratios.
  • Formulas generalize to known ensembles (grand canonical, isothermal-isobaric).
  • Numerical validation using an Ising model confirms theoretical predictions.

Conclusions:

  • The derived ensemble provides a unified framework for open systems.
  • It offers a deeper understanding of thermodynamic system behavior.
  • The approach is consistent with established thermodynamic theories.