Irreversible microscopic processes (viz intrinsic stochasticities), i.e. processes in which a unitary dynamical group is related to a semi-group of contracting maps, are considered for the following examples: the shift in w.r.t. random walks; the shift in w.r.t. diffusion; the nonrelativistic free Hamiltonian and the relativistic free Hamiltonian of scalar spin-zero particles with rest-mass w.r.t. the corresponding contractive semi-group generated by these operators. The last example is also considered in the context of a particle–antiparticle system, thereby exhibiting an asymmetry between the number of particles and antiparticles. The positive and negative parts of the Hamilton operator of the Dirac equation are calculated and related to an intrinsic stochasticity. For classical Hamiltonian systems an intrinsic stochasticity is defined and applied to examples. Reverse processes and measurements connected with intrinsic stochasticity are defined.