Density-functional fluctuation theory of crowds.

Area of Science:

• Collective behavior studies
• Statistical physics
• Biophysics

Background:

• Predicting crowd behavior is crucial for understanding emergent phenomena.
• Current models either describe behaviors (top-down) or postulate rules (bottom-up).
• A data-driven approach is needed to directly determine predictive rules.

Purpose of the Study:

• To develop a theory-based, data-driven method for predicting collective population behavior.
• To quantify the rules governing crowd distributions directly from local density observations.
• To demonstrate the method's predictive power in a model system.

Main Methods:

• Classical density functional theory (DFT) was employed.
• Local crowd density observations were used to extract spatial and social preference functions.
• A model crowd of walking fruit flies was used for demonstration.

Main Results:

• The developed DFT approach accurately predicts experimental fly distributions in novel environments.
• Two key functions quantifying spatial and social preferences were extracted.
• The method provides a quantitative measure of crowd "mood".

Conclusions:

• The theory-based, data-driven DFT approach successfully predicts collective behaviors.
• This method offers a new way to quantify and predict crowd dynamics.
• The approach has potential applications in diverse fields like ecology, active matter, demography, and economics.