If two systems, S a and S b , have identical intensive variables, a thermodynamic operation of wall removal can compose them into a single system, S, with the same intensive variables. If, for example, their internal energies are in the ratio λ :(1− λ), then the composed system, S, has internal energy in the ratio of 1: λ to that of the system S a. By the inverse thermodynamic operation, the system S can be split into two subsystems in the obvious way. As usual, these thermodynamic operations are conducted in total ignorance of the microscopic states of the systems. More particularly, it is characteristic of macroscopic thermodynamics that the probability vanishes, that the splitting operation occurs at an instant when system S is in the kind of extreme transient microscopic state envisaged by the Poincaré recurrence argument. Such splitting and recomposition is in accord with the above defined additivity of extensive variables.