The Lieb-Yngvason theory of thermodynamics

The structure of thermodynamics follows from the existence of an extensive, additive, and concave entropy function. Yet despite the centrality of entropy in the theory, it is often introduced in a roundabout way via heat engines, or by invoking notions from statistical mechanics. Attempts during the during the 20^thcentury to formulate a conceptually self-contained and mathematically rigorous version of thermodynamics culminated in the work of Lieb and Yngvason in 1999. They show that a certain physically intuitive notion of ‘adiabatic accessibility’ is mathematically equivalent to the existence of a unique entropy function with the desired properties. This modern understanding of thermodynamics is also relevant to understanding why nonequilibrium physics cannot be similarly encapsulated by an entropy principle. I will introduce this theory to the audience.