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 $I\left[p\right]$ and the FI channel capacity 〈I〉. These are shown to be linearly related to the partition function Z, the coherence function $\rho {(x,x}^{\prime }),$ the two-point coherence function $\tau \left(\Delta x\right),$ the entropy of fluctuation $H\left(\Delta x\right),$ and the cross entropy $H_{\mathrm{KL}}\left(\rho {/r}_{\Delta }\right)$ between the system probability density function $\rho \mathrm{}(x,x)\mathrm{}$ and its shifted version $\rho (x+\Delta x,x+\Delta x).\mathrm{}$

• Received 2 May 2002

DOI:https://doi.org/10.1103/PhysRevA.66.022107