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Extreme physical information (EPI) is a principle, discovered by B. Roy Frieden, for discovering scientific laws taking the form of differential equations and probability distribution functions. Examples include the Schrödinger wave equation and the Maxwell-Boltzmann distribution law. EPI can be seen as an extension of information theory to encompass much, and perhaps all, of theoretical physics and chemistry.

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. Moreover, the random errors that contaminate the observations are presumed to define the probability distribution function of the source phenomenon. That is, "the physics lies in the fluctuations." Finally, the information loss can be shown to be an extreme value. Thus, if the Fisher information in the data is I, and the Fisher information in the source is J, the EPI principle states that I − J = extremum. The extremum for most situations is a minimum, meaning that there is a comforting tendency for any observation to describe its source faithfully. EPI can also be seen as a game against nature. While this game-theoretic structure is only a manner of speaking, Frieden shows that it has explanatory power.

Frieden (2004: 81-84) grounds EPI in three axioms:

• Law of Conservation of information change. Let an act of observation perturb a source and the data gathered from that source. Let the perturbed information be δI and δJ. Then δI = δJ.
• There exist sequences of functions ${\displaystyle i_{n}(x)}$ and ${\displaystyle j_{n}(x)}$ such that ${\displaystyle I=\int \sum _{n}i_{n}(x)\,dx}$ and ${\displaystyle J=\int \sum _{n}j_{n}(x)\,dx.}$
• Microscopic zero condition. ${\displaystyle \exists \kappa ,0<\kappa <1,}$ such that ${\displaystyle i_{n}(x)-\kappa j_{n}(x)=0.}$

Frieden (2004) employs EPI to derive a number of fundamental laws of physics, as well as some established principles and new laws of biology, the biophysics of cancer growth, chemistry, and economics. Fisher information, in particular the loss I - J resutling from observation, is a powerful new method for deriving laws governing many aspects of nature and human society.

References

• B. Roy Frieden (2004) Science from Fisher Information, 2nd ed. Cambridge University Press.
• Frieden, BR and RJ Hughes (1994) "Spectral 1/f noise derived from extremized physical information." Phys. Rev. E 49, 2644
• Frieden, BR and BH Soffer (1995) "Lagrangians of physics and the game of Fisher-information transfer." Phys. Rev. E 52, 2274
• Frieden, BR and RA Gatenby (2004) "Information dynamics in carcinogenesis and tumor growth." Mutat. Res. 568, 259
• Hawkins, RJ, Frieden, BR and JL D'Anna (2005) "Ab initio yield curve dynamics." Phys. Lett. A 344, 317
• Frieden, BR and RA Gatenby (2005) "Power laws of complex systems from extreme physical information." Phys. Rev. E 72, 036101

External links

• B. Roy Frieden, "Fisher Information, a New Paradigm for Science: Introduction, Uncertainty principles, Wave equations, Ideas of Escher, Kant, Plato and Wheeler." This essay is continually revised in the light of ongoing research.
• The Bactra Review A critical review of Frieden's book in particular, and Extreme Physical Information in general.
• See in-depth review "An Unexpected Union - Physics and Fisher Information" in SIAM News at

• Estimation theory
• Information theory