Extreme physical information


Extreme physical information is a principle in information theory, first described and formulated in 1998 by B. Roy Frieden, Emeritus Professor of Optical Sciences at the University of Arizona. The principle states that the precipitation of scientific laws can be derived through Fisher information, taking the form of differential equations and probability distribution functions.

Introduction

Physicist John Archibald Wheeler stated that:
By using Fisher information, in particular its loss I - J incurred during observation, the EPI principle provides a new approach for deriving laws governing many aspects of nature and human society. EPI can be seen as an extension of information theory that encompasses much theoretical physics and chemistry. Examples include the Schrödinger wave equation and the Maxwell–Boltzmann distribution law. EPI has been used to derive a number of fundamental laws of physics, biology, the biophysics of cancer growth,chemistry, and economics. EPI can also be seen as a game against nature, first proposed by Charles Sanders Peirce. The approach does require prior knowledge of an appropriate invariance principle or data.

EPI principle

The EPI principle builds on the well known idea that the observation of a "source" phenomenon is never completely accurate. That is, information present in the source is inevitably lost when observing the source. The random errors in the observations are presumed to define the probability distribution function of the source phenomenon. That is, "the physics lies in the fluctuations." The information loss is postulated to be an extreme value. Denoting the Fisher information in the data as, and that in the source as, the EPI principle states that
Since the data are generally imperfect versions of the source, the extremum for most situations is a minimum. Thus there is a comforting tendency for any observation to describe its source faithfully. The EPI principle may be solved for the unknown system amplitudes via the usual Euler-Lagrange equations of variational calculus.

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