Quantifying system order for full and partial coarse graining

Frieden, B. Roy; Hawkins, Raymond J.

doi:10.1103/physreve.82.066117

Cited by 22 publications

(46 citation statements)

References 22 publications

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“…It is this very interaction, causing an irreversible exchange of information and energy with those of the system, that gives rise to the output measurement. Its irreversible nature amounts to a lossy, or "coarse-grained" [6,[26][27][28], process. Assume such a measurement to be made of a system with ideal Fisher information level J.…”

Section: Observation Is a Generally Lossy Processmentioning

confidence: 99%

Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation

Frieden

2015

Entropy

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Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q 2 (x). Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering the flow of Fisher information J → I from source effect to observer that occurs during macroscopic observation of the system. Such an observation is irreversible and, hence, incurs a general loss I − J of the information. By requiring stability of the law q(x), as well, it is found to obey a principle I − J = min . of "extreme physical information" (EPI). Information I is the same functional of q(x) for any shift-invariant system, and J is a functional defining a physical source effect that must be known at least approximately. The minimum of EPI implies that I ≈ J or received information tends to well-approximate reality. Past applications of EPI to predicting laws of statistical physics, chemistry, biology, economics and social organization are briefly described.

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Section: Observation Is a Generally Lossy Processmentioning

confidence: 99%

Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation

Frieden

2015

Entropy

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“…The concept of the level of Order in a continuous system has been quantified [9,10] Hence the order is linear in Fisher information I, the latter defined by Eq. (1).…”

Section: What Is Order?mentioning

confidence: 99%

“…Also, L is the maximum chord length connecting two surface points of the system (effectively the diameter of the cell). Examples in [9,10] show that I and R also serve to measure the level of "complexity" in the system. (For example, a system with purely sinusoidal structure in all dimensions has a level of Order going as the square of the total number of sinusoidal wiggles in the system.…”

Section: What Is Order?mentioning

confidence: 99%

Cell Development Pathways Follow from a Principle of Extreme Fisher Information

Gatenby¹

2012

J Physic Chem Biophysic

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Background: In a normally developing eukaryote, information arrives at the cell membrane in the form of a ligand that binds to a protein receptor. This initiates a cascade of biochemical events causing one or more proteins to subsequently traverse the cell cytoplasm to the nucleus. This defines a communication channel. What does it accomplish?Method: The protein traversals transfer to the nucleus maximum Fisher information about the spatial and temporal coordinates of the ligand binding sites. This hypothesis implies a cell model of fast, largely-directed, protein movement dominated by Coulomb interaction with intracellular electric fields. It makes the following predictions: (1) Very high intracellular electric field strengths, typically tens of millions of volts/meter (2) A central role for negative charges added to proteins by phosphorylation, in promoting their Coulomb force-dominated motion toward the nucleus; (3) The dominance of protein pathways consisting of from 1-4 proteins, e.g. the RAF, RAS and MEK pathways; (4) A predicted fast response (2,800 proteins/ms) of cells to sudden trauma such as wounds; (5) A predicted 4nm size (9) for the EGFR protein. (6) Logic mechanisms in the nucleus for optimally deconvolving spatial and temporal binding site values from the inflowing messenger proteins.Results: Predictions (1-5) are supported by laboratory observations. Conclusions:Living systems achieve stably ordered and complex states by maintaining extreme levels of Fisher information. The attained order values increase from cancers to prokaryotes to eukaryotes to multicellular organisms. In eukaryotes this fosters maximally high protein flux rates at the nucleus which, in turn, optimize wired-in intranuclear logic mechanisms for processing this, and other, temporal and spatial information.

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“…Among its many properties, one of the most important ones is that FIM is a measure of order, as opposed to disorder, best represented by the Gibbs-Boltzmann-Shannon (GBS) entropy S [2]. Information theory (IT), pioneered by Shannon, is able to tell us in precise fashion the information-content of a probability distribution function (PDF) P(i) (i = 1, .…”

Section: Introductionmentioning

confidence: 99%

The Fisher Thermodynamics of Quasi-Probabilities

Pennini

Plastino

2015

Entropy

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Abstract:With reference to Lee's treatment of quasi-probabilities, it is seen that the three phase space quasi-probabilities, known as the P-, Husimi and Wigner ones, plus other intermediate ones, generate a common, single Fisher thermodynamics, along the lines developed by Frieden et al. We explore some facets of such thermodynamics and encounter complementarity between two different kinds of Fisher information.

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Quantifying system order for full and partial coarse graining

Cited by 22 publications

References 22 publications

Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation

Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation

Cell Development Pathways Follow from a Principle of Extreme Fisher Information

The Fisher Thermodynamics of Quasi-Probabilities

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