with (2) is the irreversible time evolution of the isolated quantum system (von Neumann equation). The term $\delta H
\varrho$ represents some complicated external effects upon the non-isolated system. With this term (1) is the standard way of describing extrinsic irreversibility due to the effect of an external reservoir $R$ (e.g., measuring apparatus) upon the system. This irreversible time evolution is described by a semigroup $\rho(t)=\Lambda(t)\rho(0)$ generated by the Liouvillian $L$, $\Lambda(t)=\mbox{e}^{Lt}$, $t\geq0$. Equation (1) has also been applied to the time evolution of such microphysical systems as the $K_L - K_S$ meson system [@R3].

That a fundamental concept like irreversibility should be caused by extrinsic influences has been considered unsatisfactory by many people working on irreversibility and statistical physics. According to Prigogine’s ideas [@R4], irreversibility should be intrinsic to the dynamics and should have its origin in the resonances (Poincaré resonances) rather than being caused by merely external effects of a quantum reservoir or the irreversible act of a measurement apparatus. This requires also a dynamical semigroup which, however, should be generated by the Hamiltonian $H$, $\rho(t)=\mbox{e}^{-iHt}\rho(0)
\mbox{e}^{iHt}$, and not by a Liouvillian like (2).

The idea of intrinsic irreversibility and the empirical facts of resonances can both be 