# Extreme physical information

**Extreme physical information** (**EPI**) is a principle, first described and formulated in 1998^{[1]} by B. Roy Frieden, Emeritus Professor of Optical Sciences at the University of Arizona, that states, 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:

All things physical are information-theoretic in origin and this is a participatory universe... Observer participancy gives rise to information; and information gives rise to physics.

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,^{[2]}^{[3]} biology,^{[4]} the biophysics of cancer growth,^{[5]}chemistry,^{[5]} and economics.^{[6]} 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.

## Books

- Frieden, B. Roy -
*Physics from Fisher Information: A Unification*, 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998 - Frieden, B. Roy -
*Science from Fisher Information: A Unification*, 2nd Ed. Cambridge University Press, ISBN 0-521-00911-1, pp502, 2004 - Frieden, B.R. & Gatenby, R.A. eds. -
*Exploratory Data Analysis Using Fisher Information*, Springer-Verlag (in press), pp358, 2006

## Recent papers using EPI

- Frieden, B. Roy & Gatenby, Robert A - "Principle of maximum Fisher information from Hardy's axioms applied to statistical systems", Phys. Rev. E 88, 042144,1-6, 2013

- Gatenby, Robert A. & Frieden, B. Roy - "Application of Information Theory and Extreme Physical Information to Carcinogenesis", :Cancer Research 62, 3675-3684, July 1, 2002

- Chimento,L.P. & Pennini, F. & Plastino, A. - "Naudts-like duality and the Extreme Fisher information principle",

- Phys. Rev. E 62, 7462-7465, 2000
- http://prola.aps.org/abstract/PRE/v62/i5/p7462_1subj: statistical mechanics

- Nagy, A. - "Fisher information in density functional theory,", J. Chem. Phys. 119, 9401-9405, 2003

- http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000119000018009401000001&idtype=cvips&gifs=yes
- Subj: The Euler equation of density functional theory is derived using EPI.

- Anton, M. & Weisen, H. & Dutch, M.J. - "X-ray tomography on the TCV tokamak",

- Plasma Phys. Control. Fusion 38, 1849-1878, 1996
- http://ej.iop.org/links/q80/fVFo+Bx3KRlwd6qcdU2Saw/p61101.pdf

- Mlynar, J. & Bertalot, L. - "Neutron spectra unfolding with minimum Fisher regularization"

- http://pos.sissa.it/archive/conferences/025/063/FNDA2006_063.pdf
- Subj: Diagnosis of plasma shape within the tokamak fusion machine using reconstructions based upon EPI.

- Venkatesan, Ravi. - "Information encryption using a Fisher-Schrödinger Model",

- Presented at 6th International Conference on Complex Systems (ICCS) June, 2006
- Boston, Massachusetts Full paper is in Frieden and Gatenby, 2006
- http://necsi.edu/community/wiki/index.php/ICCS06/235
- Subj: Encryption, secure transmission using EPI, in particular game aspect.

- Fath B.D. & Cabezas, H. & CW Pawlowski - "Exergy and Fisher information as ecological indices",

- Ecological Modeling 174, 25-35, 2004 - CW 2003
- http://zp9vv3zm2k.scholar.serialssolutions.com/sid=google&auinit=BD&aulast=Fath&atitle=Exergy+and+Fisher+Information+as+ecological+indices&id=doi:10.1016/j.ecolmodel.2003.12.045
- Subj: monitoring of the environment for species diversity

- Yolles. M.I. - "Knowledge Cybernetics: A New Metaphor for Social Collectives", 2005

- http://isce.edu/ISCE_Group_Site/web-content/ISCE_Events/Christchurch_2005/Papers/Yolles.pdf
- Subj: Information-based approaches to knowledge management.

- Venkatesan, R.C. - "Invariant Extreme Physical Information and Fuzzy Clustering", Proc. SPIE Symposium on Defense & Security,

- Intelligent Computing: Theory and Applications II, Priddy, K. L. ed, Volume 5421, pp. 48-57, Orlando, Florida, 2004
- http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PSISDG005421000001000048000001&idtype=cvips&prog=normal

- Ménard, Michel. & Eboueya, Michel. - "Extreme physical information and objective function in fuzzy clustering",

- Fuzzy Sets and Systems 128(3): 285-303, 2002
- http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V05-45SR1TJ-1-1&_cdi=5637&_user=56761&_orig=na&_coverDate=06%2F162F2002&_sk=998719996&view=c&wchp=dGLbVlz-zSkWb&md5=4280259595b947a7b560f634f47de5c4&ie=/sdarticle.pdf

- Ménard,Michel. & Dardignac, Pierre-André. & Chibelushi, Claude C. - "Non-extensive thermostatistics and

- extreme physical information for fuzzy clustering (invited paper)", IJCC, 2 (4): 1-63, 2004
- http://www.yangsky.us/ijcc/pdf/ijcc241.pdf

## See also

## Notes

- ↑ B. Roy Frieden,
*Physics from Fisher Information: A Unification*, 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998 ([ref name="Frieden6"] shows 2nd Ed.) - ↑ Frieden, B.R. & Hughes, R.J.,
*Spectral 1/f noise derived from extremized physical information*,*Phys. Rev. E***49,**2644, 1994 - ↑ Frieden, B.R. & Soffer, B.H.,
*Lagrangians of physics and the game of Fisher-information transfer*,*Phys. Rev. E***52,**2274, 1995 - ↑ Frieden, B.R., & Plastino, A. & Soffer, B.H.,
*Population genetics from an information perspective*,*J. Theor. Biol.***208,**49-64, 2001 - ↑
^{5.0}^{5.1}Frieden, B.R. & Gatenby, R.A. -*Information dynamics in carcinogenesis and tumor growth*,*Mutat. Res.***568,**259, 2004 - ↑ Hawkins, R.J. & Frieden, B.R. & D'Anna, J.L. -
*Ab initio yield curve dynamics*,*Phys. Lett. A***344,**317, 2005

## References

- Frieden, B.R. -
*Fisher information as the basis for the Schrödinger wave equation*, Am. J. Physics**57**, 1004-1008, 1989 - Frieden, B.R. -
*Fisher information, disorder, and the equilibrium distributions of physics*, Phys. Rev. A**41**, 4265-4276, 1990 - Frieden, B.R. -
*Estimation of distribution laws, and physical laws, by a principle of extremized physical information*, Physica A**198**, 262-338, 1993 - Frieden, B.R. -
*Physics from Fisher Information*, Mathematics Today**37**, 115-119, 2001 - Frieden, B.R. & Gatenby, R.A. -
*Power laws of complex systems from extreme physical information*,*Phys. Rev. E***72,**036101, 2005 - Frieden, B.R. & Soffer, B.H. -
*Information-theoretic significance of the Wigner distribution*,*Phys. Rev. A*, to be published 2006

## 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 using EPI.
- The Bactra Review A critical review of the first edition of
*Science from Fisher Information*(2nd ed. listed above), and on EPI in general. - Unexpected Union - Physics and Fisher Information: An uncritical review of the same book and an introduction to EPI from SIAM News Vol 33 #6; July 17, 2000