Vorlesungsbeschreibung
The course Statistical Thermodynamics I covers the statistical foundations of thermodynamics. The exercise sets are an integral part of the course and include, among other things, derivations that are not carried out in the script. The lecture is divided into three parts.
Part I: Classical Thermodynamics
The course begins with an introduction to classical thermodynamics and its key concepts. Thermodynamics (or heat theory) deals with macroscopic systems. It is a phenomenological theory, directly motivated by experimental results and verifiable through experiments. Although it does not explicitly rely on the atomic structure of matter, its statements are generally valid.
The laws of thermodynamics are empirical principles from which classical thermodynamics can be developed in a consistent manner; in this sense, they are comparable to mathematical axioms. While thermodynamic statements are phenomenological in nature, it is now possible to justify them using quantum mechanics and statistical arguments. Nevertheless, thermodynamic concepts remain of great practical and theoretical importance. From the perspective of the renormalization group, thermodynamics can be interpreted as an effective theory that correctly describes the phenomenology of macroscopic systems at low energy scales.
Part II: Statistical Mechanics
The second part introduces statistical mechanics. This framework studies systems composed of many microscopic particles and derives their macroscopic behavior using statistical methods, thus starting from the atomic picture of matter. Statistical mechanics provides a foundation for the laws of thermodynamics and allows thermodynamic properties of macroscopic systems to be derived from their microscopic characteristics. Even a single mole of gas contains on the order of 10^23 particles. Tracking their individual positions and velocities is both practically impossible and theoretically unnecessary. Statistical mechanics exploits the fact that, for macroscopic systems, statistical averages coincide with experimentally measurable quantities.
After a brief introduction to probability and statistics, various statistical ensembles are discussed and their connection to classical thermodynamics is established. It will be shown that, in the thermodynamic limit, all ensembles considered lead to the same thermodynamic results.
Part III: Applications of Statistical Thermodynamicss
Building on the theoretical and conceptual foundations developed earlier, the third part focuses on applications of statistical thermodynamics. The discussion begins with the simplest case, the ideal gas—an idealized system of point particles without interactions—which serves as a clear illustration of the core concepts. This is followed by generalizations of the ideal gas that reflect various properties of a real gas, such as the dilute classical gas and the diatomic ideal gas. Finally, an ideal spin system is introduced as a model for the behavior of a paramagnet.
