Statistical mechanics is the branch of physics that applies probability theory and statistics to describe the behavior of systems with a large number of particles. It provides a framework for understanding macroscopic phenomena in terms of the microscopic properties of individual particles. The central goal of statistical mechanics is to connect the microscopic world of atoms and molecules with the macroscopic world of thermodynamic variables like temperature, pressure, and volume.

Historically, statistical mechanics emerged in the 19th century as scientists sought to explain the observed laws of thermodynamics, which describe the behavior of systems in equilibrium. Classical thermodynamics, while incredibly successful, was primarily phenomenological and lacked a fundamental microscopic understanding. This gap was filled by the development of statistical mechanics, largely attributed to the works of Ludwig Boltzmann, James Clerk Maxwell, and Josiah Willard Gibbs.

At its core, statistical mechanics is based on the idea that the behavior of macroscopic systems can be understood by considering the collective behavior of their microscopic constituents. Instead of directly tracking every particle, which is practically impossible for large systems, statistical mechanics calculates the statistical properties of the system. These properties are derived from the laws of probability