Relations between parameters of a decoherent system and Fisher information

Fisher information (FI) is normally developed and applied within the context of classical mathematical statistics. Here we show that it alternatively arises as physical properties of a generally decoherent system. Two kinds of Fisher information are treated: the classical FI $I[p]$ and the FI channel capacity 〈I〉. These are shown to be linearly related to the partition function Z, the coherence function ρ(x,x^'), the two-point coherence function τ(Δx), the entropy of fluctuation H(Δx), and the cross entropy HKL(ρ/r_Δ) between the system probability density function ρ(x,x) and its shifted version ρ(x+Δx,x+Δx).