Statistical Mechanics: How Probability and Statistics Explain Molecular Behavior in Physics

This paper examines how statistical mechanics employs probability and statistics to explain the collective behavior of microscopic particles, particularly in gases. By moving beyond the limitations of deterministic models, it explores how macroscopic properties such as pressure, temperature, and entropy emerge from the random motion of atoms and molecules. Foundational concepts including Brownian motion, the Maxwell-Boltzmann distribution, mean free path, and Boltzmann’s H-theorem are discussed to illustrate the statistical nature of thermodynamic behavior. The study also introduces phase space formalism and major statistical models; Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein, to demonstrate how order arises from molecular chaos at both classical and quantum levels.