This contribution is dedicated to dilucidating the role of the Gibbs entropy
in the discussion of the emergence of irreversibility in the macroscopic world
from the microscopic level. By using an extension of the Onsager theory to the
phase space we obtain a generalization of the Liouville equation describing the
evolution of the distribution vector in the form of a master equation. This
formalism leads in a natural way to the breaking of the BBGKY hierarchy. As a
particular case we derive the Boltzmann equation
