1. Context and origins The object of thermodynamics is to describe “macroscopic” systems (systems that are extended in space) that vary slowly in time. Macroscopic systems are formed by a huge number of microscopic particles; for instance, a gallon of gas contains about 1023 molecules. But thermodynamics does not depend on the underlying nature of the system — it was actually pioneered before the atomic hypothesis was confirmed, and before quantum phenomena were discovered. The links between the micro- and the macroscopic worlds, and how the former determines the latter, are the subject of statistical mechanics. Within thermodynamics, thermostatics is the physical theory that deals with equilibrium states, and with transformations where time is not an explicit variable; it ignores the flows, i.e. the time derivatives of quantities such as the energy or the number of particles. The origins of thermodynamics go back to the XIXth century and the industrial revolution. This was the age of steam engines, which convert heat energy into work. The law of conservation of energy implies that no more work can be produced than heat is available. The challenge was to design an engine that could convert all the energy obtained by burning coal into work. But physicists came to realize that the efficiency of steam engines was not only limited by technical nuisances such as losses due to friction, but there were fundamental constraints as well. A new basic quantity emerged, that is hard to grasp although it is present in everyday life: the