Introduction to Stochastic Thermodynamics

We introduce the framework of Stochastic Thermodynamics and learn how to precisely characterize thermodynamic quantities such as heat, work, and entropy at the level of individual particle trajectories. This framework enables the study of thermodynamic systems out of equilibrium, including their fluctuations and finite-time transitions. Specifically, we derive the second law of thermodynamics, characterizing minimum entropy production during finite-time transitions through the Optimal Transport 2-Wasserstein distance. Additionally, we study the canonical finite-time Carnot cycle, where an overdamped system is alternatingly connected to two heat baths at different temperatures for the purpose of work extraction. Within this context, we quantify both maximum power and efficiency at maximum power. Finally, we provide a brief overview of more advanced findings regarding information thermodynamics and fluctuation theorems.