A definition of entropy based entirely on the relation of adiabatic accessibility between equilibrium states was given by E. H. Lieb and J. Yngvason in 1999. This approach has several predecessors, including the pioneering work of Constantin Carathéodory from 1909 and the monograph by R. Giles. In the setting of Lieb and Yngvason, one starts by picking, for a unit amount of the substance under consideration, two reference states X 0 and X 1 such that the latter is adiabatically accessible from the former but not conversely. Defining the entropies of the reference states to be 0 and 1 respectively, the entropy of a state X is defined as the largest number λ λ such that X is adiabatically accessible from a composite state consisting of an amount λ λ in the state X 1 and a complementary amount, ( 1 − − λ λ ) , in the state X 0 . A simple but important result within this setting is that entropy is uniquely determined, apart from a choice of unit and an additive constant for each chemical element, by the following properties: it is monotonic with respect to the relation of adiabatic accessibility, additive on composite systems, and extensive under scaling.