A Study of PM2.5 Behavior in Indoor Environments Using Canonical and Grand Canonical Ensembles

Buddhi Pushpawela, JULIAN PALLINI, The University of Alabama in Huntsville

     Abstract Number: 239
     Working Group: Indoor Aerosols

Abstract
This study presents a theoretical investigation of PM2.5 aerosol dynamics in indoor environments using the framework of statistical mechanics, with a focus on the canonical and grand canonical ensembles. PM2.5 poses serious health risks, especially in enclosed or poorly ventilated spaces with significant accumulation. Traditional macroscopic models often neglect the microscopic thermodynamic fluctuations relevant to such confined systems.

In this work, we modeled unventilated indoor spaces using the canonical ensemble, where the particle number, volume, and temperature are fixed, and ventilated environments using the grand canonical ensemble, which allows for fluctuations in particle number due to particle exchange with the surroundings. Simulated monthly PM 2.5 concentration data for both ventilated and unventilated conditions are used to parameterize models. Using the canonical partition function, we derived expressions for internal energy, entropy, and the distribution of microstates. The grand partition function is employed to compute the chemical potential, average particle number, and entropy as functions of environmental parameters such as ventilation rate and particle influx. This ensemble-based approach provides a theoretical framework for understanding the thermodynamic behavior of particles in confined indoor systems. By linking microscopic statistical mechanics with macroscopic environmental conditions, our study provided insights into how ventilation influences aerosol stability, particle fluctuations, and system equilibrium. This work also highlights the importance of ensemble selection in modeling real-world finite systems and demonstrates the value of statistical mechanics in addressing the challenges in indoor air quality.