Fisher Information as a Measure of Time

Author: Frieden, B.R.

Source: Astrophysics and Space Science, Volume 244, Numbers 1-2, 1996 , pp. 387-391(5)

Publisher: Springer

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Fisher information I is a classical concept that originates in estimation theory. Through the Cramer-Rao inequality, it defines the smallest possible error in the estimation of a parameter in the presence of noise obeying a given probability law. More recently, Fisher information has been incorporated within a variational principle for forming the laws of physics (Schrödinger wave equation, Dirac equation, etc.). The premise is that dI/dt ≤ 0, with t the time, so that, at equilibrium, I = min. The premise has recently been proven for any process obeying a Fokker-Planck differential equation. Hence, Fisher information provides a new measure of the passage of time. All errors of estimation increase, on average, with time.

Document Type: Regular Paper

Affiliations: Optical Sciences Center University of Arizona Tucson, Arizona 85721-0094

Publication date: January 1, 1996

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