Introduction to Nonequilibrium Statistical Mechanics

Most physical systems in the real world are constantly in motion, exchanging energy and matter with their surroundings. While classical thermodynamics focuses on static equilibrium, understanding real-world processes requires a deep dive into nonequilibrium states. This text-only course provides a clear, conceptual pathway into the mathematical and physical frameworks used to model systems out of thermal equilibrium. By reading through these structured lessons, you will transition from basic transport concepts to advanced stochastic modeling, gaining the tools needed to analyze dynamic physical, chemical, and biological systems. What you'll learn: - Understand the fundamental differences between equilibrium and nonequilibrium states, including local equilibrium assumptions. - Model random physical processes using the Langevin equation and Brownian motion concepts. - Master the Fokker-Planck equation and master equations to describe the evolution of probability distributions. - Apply linear response theory, the fluctuation-dissipation theorem, and Green-Kubo relations to transport phenomena. - Explore modern fluctuation theorems, including the Jarzynski equality and Crooks fluctuation theorem. - Analyze Markov processes and random walks as foundational tools for statistical modeling. We begin with essential terminology, basic probability concepts, and classic transport equations before progressing to stochastic dynamics and modern thermodynamic relations. This course is ideal for undergraduate or early graduate students in physics, chemistry, or engineering who have a basic grasp of thermodynamics and want to expand their analytical toolkit. Start reading today to unlock the principles governing the dynamic, non-equilibrium universe.