Abstract

The principle of minimum Fisher information (MFI) provides a basis for deriving most of the laws of physics.¹ The Fisher I is defined as (mean-squares error)^-1 in the efficient determination of the classical position θ of a particle. For a one-component pdf p(x) = q²(x), the Fisher information is a one-term functional I = 4 ʃdx[q’(x)]². Thus, I decreases as q(x) becomes smoother, or as disorder increases, consistent with the second law of thermodynamics. In the above, p(x) was specifically assumed to have a single component q²(x). Then MFI gives a real-only wave equation. Here we consider multicomponent cases p(x) = q₁²(x) + … + q_N²(x), where the q_n(x) are independent degrees of freedom. We seek the Fisher I for the case N = 2 of nonrelativistic quantum mechanics or of scalar optics. A benchmark statistical situation arises when the N components of q_n(x) do not overlap. Then their informations add, and the resulting mean-squares error value is efficient, i.e. an absolute minimum.

© 1991 Optical Society of America