The Fundamentals of Thermodynamics

The aim of this text is to provide an account of the fundamentals of thermodynamics which is accessible at graduate level to physicists, mathematicians and philosophers of physics. The bulk of the book (Chapters 2-9) is based on the algebraic approach of Lieb and Yngvason, but extended to encompass both positive and negative temperatures and systems in which entropy increases and decreases in adiabatic processes. We show that these four possibilities are already present in Carathéodory's ve...