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This study explores pressure correlations in solids and fluids using coarse-grained models. It reveals a universal scaling law for the compression modulus across different thermodynamic ensembles.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Understanding pressure and its contributions (ideal and excess) is crucial for characterizing materials.
  • Coarse-grained models simplify complex systems, enabling the study of bulk properties like compressibility.
  • Ensemble theory (NPT and NVT) provides frameworks for simulating systems under different constraints.

Purpose of the Study:

  • To investigate correlations of instantaneous pressure and its components in isotropic solids and fluids.
  • To derive and analyze the stress fluctuation representation of the compression modulus.
  • To explore the crossover between NPT and NVT ensembles using a generalized constraint parameter.

Main Methods:

  • Development and application of simple coarse-grained models in 1, 2, and 3 dimensions.
  • Utilizing NPT and NVT ensembles with a variable constraint parameter (λ).
  • Applying thermodynamic transformation rules between conjugated ensembles.
  • Computing the Rowlinson functional and analyzing its relation to the compression modulus.

Main Results:

  • A direct derivation of the compression modulus (K) in the NVT ensemble using stress fluctuations.
  • Identification of a universal scaling variable x = P_id/K, where P_id is the ideal pressure.
  • Demonstration of a universal function f0(x) = x(2-x) relating the Rowlinson functional to K.
  • Observation of a crossover behavior between the NPT and NVT ensembles governed by a lever rule.

Conclusions:

  • The study establishes a unified framework for understanding material compressibility across different ensembles.
  • The derived universal scaling law and function offer predictive power for material behavior.
  • Coarse-grained models effectively capture essential thermodynamic properties, bridging microscopic details and macroscopic behavior.