"Linearly time-dependent information on invariant set"
In this paper a family of information I(b) with a parameter b is introduced and the reason why its coarse-grained information Ic(b) becomes to be independent of b near t=0, i.e. the probability density on the invariant set is uniformized and Ic(b) shows linearly time-dependent behavior, was theoretically examined. If the time-dependent probability measure of coarse-grained systems is described by a master equation (ME), a diffusion effect is necessarily brought into the systems, and the uniformization is caused by the information production originated from the diffusion effect. The production is completely corresponds to the entropy production, which is generally related to the phase space volume contraction rate in dissipative systems, and, therefore, the phenomena can be observed for a wide class of dynamical systems as irreversible processes go.