Entropy of level-cut random Gaussian structures at different volume fractions

Area of Science:

• Statistical Physics
• Materials Science
• Physical Chemistry

Background:

• Random Gaussian fields are used to model diverse physical systems with multiple phases.
• The entropy of these structures is linked to the generating field's covariance and spectral density.
• Previous studies overlooked the impact of phase volume fractions on entropy.

Purpose of the Study:

• To investigate the influence of phase volume fractions on the entropy of level-cut Gaussian random field structures.
• To determine if this dependence deviates from established theoretical models.
• To explore the implications for understanding complex fluid and microemulsion systems.

Main Methods:

• Evaluation of entropy for several lattice models.
• Analysis of level-cut structures derived from Gaussian random fields.
• Comparison of results with ideal noninteracting system formulas.

Main Results:

• The entropy of level-cut structures is significantly influenced by the volume fractions of different phases.
• This dependence scales consistently with the formula for ideal noninteracting systems, even in strongly coupled systems.
• The cutting level selection directly impacts phase composition and overall entropy.

Conclusions:

• The entropy of multi-phase structures generated by level-cut Gaussian fields exhibits a universal scaling behavior with molar fractions.
• This finding simplifies the understanding of entropy in complex systems, regardless of inter-component interactions.
• The results have direct applications in modeling binary/ternary fluids and microemulsions.