Extreme physical information
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Extreme physical information (EPI) is a principle, first described and formulated in 1998 [3] 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 the loss I - J incurred during observation, the EPI principle provides a powerful 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 [1][2], biology [4], the biophysics of cancer growth [5], chemistry [5], and economics [7]. EPI can also be seen as a game against nature, first proposed by Charles S. Peirce. The approach does require prior knowledge of an appropriate invariance principle or data.Some critics regard the theory as vague and ill-defined. For example, the location of the extremum may depend on the coordinate system used to model the physical objects.
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], and the Fisher information in the source is [\mathcal], the EPI principle states that:
- [\mathcal-\mathcal=\mathrm ]
The extremum for most situations is a minimum, meaning that there is a comforting tendency for any observation to describe its source faithfully.
References
[1]. Frieden, B.R. & Hughes, R.J. - Spectral 1/f noise derived from extremized physical information, Phys. Rev. E 49, 2644, 1994
[2]. Frieden, B.R. & Soffer, B.H. - Lagrangians of physics and the game of Fisher-information transfer, Phys. Rev. E 52, 2274, 1995
[3]. Frieden, B. Roy - Science from Fisher Information: A Unification , 1st Ed. Cambridge University Press, ISBN 052163167X, pp328, 1998
[4]. Frieden, B.R., & Plastino, A. & Soffer, B.H. - Population genetics from an information perspective, J. Theor. Biol. 208, 49-64, 2001
[5]. Frieden, B.R. & Gatenby, R.A. - Information dynamics in carcinogenesis and tumor growth, Mutat. Res. 568, 259, 2004
[6]. Frieden, B. Roy - Science from Fisher Information: A Unification , 2nd Ed. Cambridge University Press, ISBN 0521009111, pp502, 2004
[7]. Hawkins, R.J. & Frieden, B.R. & D'Anna, J.L. - Ab initio yield curve dynamics, Phys. Lett. A 344, 317, 2005
[8]. Frieden, B.R. & Gatenby, R.A. - Power laws of complex systems from extreme physical information, Phys. Rev. E 72, 036101, 2005
[9]. Frieden, B.R. & Gatenby, R.A. eds. - Exploratory Data Analysis Using Fisher Information, Springer-Verlag (in press), 2006
Books
- Frieden, B. Roy - Science from Fisher Information: A Unification , 1st Ed. Cambridge University Press, ISBN 052163167X, pp328, 1998
- Frieden, B. Roy - Science from Fisher Information: A Unification , 2nd Ed. Cambridge University Press, ISBN 0521009111, pp502, 2004
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]
Recent papers using EPI
- 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”,
- Nagy, A. - “Fisher information in density functional theory,”, J. Chem. Phys. 119, 9401-9405, 2003
- Anton, M. & Weisen,H. & Dutch, M.J. - “X-ray tomography on the TCV tokamak”,
- Mlynar, J. & Bertalot, L. - “Neutron spectra unfolding with minimum Fisher regularization”
- Venkatesan, Ravi. - “Information encryption using a Fisher-Schroedinger Model”,
- Fath B.D. & Cabezas, H. & CW Pawlowski - “Exergy and Fisher information as ecological indices”,
- Yolles. M.I. - “Knowledge Cybernetics: A New Metaphor for Social Collectives”, 2005
- Venkatesan,R.C. - “Invariant Extreme Physical Information and Fuzzy Clustering”, Proc. SPIE Symposium on Defense & Security,
- Ménard,Michel. & Dardignac,Pierre-André. & Chibelushi,Claude C. - "Non-extensive thermostatistics and
Further helpful reading
- Frieden, B.R - Fisher information as the basis for the Schrodinger 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
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