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Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures.

Joshua Matthes1, Silas Robitschko1, Johanna Müller1

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We introduce gauge invariance for classical multi-component systems, yielding exact equilibrium sum rules. This framework reveals novel correlation functions and provides practical tools for analyzing complex mixtures.

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Area of Science:

  • Statistical Mechanics
  • Theoretical Physics
  • Computational Chemistry

Background:

  • Classical multi-component systems require robust theoretical frameworks for equilibrium analysis.
  • Gauge invariance is a fundamental concept in physics, but its application to statistical mechanics is complex.
  • Understanding interparticle interactions and system dynamics is crucial for predicting material properties.

Purpose of the Study:

  • To formulate gauge invariance for equilibrium statistical mechanics of classical multi-component systems.
  • To develop a theoretical framework yielding exact equilibrium sum rules and novel correlation functions.
  • To demonstrate the practical applicability of the developed framework using computational simulations.

Main Methods:

  • Formulation of gauge invariance using species-resolved phase space shifting and Noether's theorem.
  • Analysis using shifting differential operators and derivation of exact sum rules.
  • Application of adaptive Brownian dynamics and grand canonical Monte Carlo simulations for validation.

Main Results:

  • Exact equilibrium sum rules for general mixtures derived from gauge invariance.
  • Emergence of species-resolved gauge correlation functions (force-force, force-gradient) at the two-body level.
  • Demonstration of practical accessibility for binary Lennard-Jones mixtures and confined systems.

Conclusions:

  • The developed gauge invariance framework provides exact sum rules and novel correlation functions for multi-component systems.
  • The approach is computationally accessible and applicable to realistic systems, including confined mixtures.
  • This work offers a powerful new tool for theoretical and computational studies in statistical mechanics and materials science.