The measure cone: Irreversibility as a geometrical phenomenon

The statistical state space is discussed in terms of the geometry of normed real vector spaces with particular reference to the novel concept of direction distance. Specialization to the geometry of the measure cone and the correspondingly specialized concept of mixing distance suggest strong mutual relationship as is shown subsequently in physically required generality. Thereby, the phenomenon of irreversibility attains an interpretation that seems to be the canonical mathematical background for classical and nonclassical statistical physics.