Probabilistic kinetics following the Pauli master equation without microscopic reversibility determines an asymptotic structure of macroprocesses in a coarse-grained phase space of many degrees of freedom. The structure, which is asymptotically realized, minimizes its irreversible decay rate among various candidates. This least irreversible decay rate is consistent with the assertion for the minimum K-entropy which has been argued to apply to the nonequilibrium asymptotic state. The irreversible decay rate is a state function characteristic of macrostructure on a coarse-grained time scale. Macrofluctuations, which always appear around the asymptote as fluctuations of the state function, do not obey the central limit theorem, implying that fluctuations whose characteristic times are not less than some finite value are never excluded.