# 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. 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." The information loss is postulated to be an extreme value. Thus, if the Fisher information in the data is $\mathcal{I}$, and the Fisher information in the source is $\mathcal{J}$, the EPI principle states that:

$\mathcal{I} - \mathcal{J} = \mathrm {Extremum}$

The extremum for most situations is a minimum, meaning that there is a comforting tendency for any observation to describe its source faithfully.

## 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
http://cancerres.aacrjournals.org/cgi/content/full/62/13/3675
• 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
• 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
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

## Notes

1. ^ Frieden, B. Roy Physics from Fisher Information: A Unification , 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998 ([ref name="Frieden6"] shows 2nd Ed.)
2. ^ Frieden, B.R. & Hughes, R.J., Spectral 1/f noise derived from extremized physical information, Phys. Rev. E 49, 2644, 1994
3. ^ Frieden, B.R. & Soffer, B.H., Lagrangians of physics and the game of Fisher-information transfer, Phys. Rev. E 52, 2274, 1995
4. ^ Frieden, B.R., & Plastino, A. & Soffer, B.H., Population genetics from an information perspective, J. Theor. Biol. 208, 49-64, 2001
5. ^ a b Frieden, B.R. & Gatenby, R.A. - Information dynamics in carcinogenesis and tumor growth, Mutat. Res. 568, 259, 2004
6. ^ 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