Foundations of Statistical Mechanics

Catalog description

Noninteracting systems, statistical mechanics of solids, liquids, gases, fluctuations, irreversible processes, phase transformations. Statistical mechanics provides a set of universal principles to describe the physics of complex systems, irrespective of their microscopic details. This course is a self-contained introduction to the mathematical foundations of the subject, starting from basic concepts of probability and the dynamics of classical systems in phase space, covering topics like ergodicity, chaos, and master equations. Using this framework we systematically derive the laws of equilibrium thermodynamics and show how they are a limiting case of recently discovered fluctuation theorems that are valid arbitrarily far from equilibrium. Along the way we explore the many facets and consequences of these laws: entropy as information, universal bounds on the efficiency of engines, the fluctuation-dissipation relation and Onsager reciprocity. Finally, we connect these ideas to the quantum realm, via the physics of decoherence and quantum master equations. The course is open to students from all backgrounds who have basic familiarity with undergraduate classical and quantum physics (a previous statistical mechanics course is helpful but not necessary). Examples in class and in the problem sets highlight the broad interdisciplinary scope of statistical mechanics, from biophysics to machine learning to quantum information.