Entropy and information

Notice the sharp maximal value of Im at a critical He ( 0.32), suggesting that there exists an optimal entropy for which CAs yield large spatial and temporal correlations. Langton conjectures that this results from two competing requirements that must both be satisfied in order for an effective computational ability to exist information storage, which involves lowering entropy, and information transmission, which involves increasing entropy. 

Entropy and Information Optics, FrancisT. S. Yu Computational Methods for Electromagnetic and Optical Systems, John M. Jarem and Partha P. Banerjee Laser Beam Shaping, Fred M. Dickey and Scott C. Holswade Rare-Earth-Doped Fiber Lasers and Amplifiers Second Edition, Revised and Expanded, edited by Michel J. F. Digonnet Lens Design Third Edition, Revised and Expanded, Milton Laikin Handbook of Optical Engineering, edited by Daniel Malacara and Brian J. Thompson... 

The isomorphism of entropy and information establishes a link between the two forms of power the power to do and the power to direct what is done. 

Beautifully written discussion of the relationship between entropy and information. 

When we speak of mathematical models for biology, we usually refer to formulae (such as the Hardy-Weinberg theorem, or the Lotka-Volterra equations) that effectively describe some features of living systems. In our case, embryonic development is not described by integrals and deconvolutions, and the formulae of the reconstruction algorithms cannot be a direct description of what happens in embryos. There is however another type of mathematical model. The formulae of energy, entropy and information, for example, apply to all natural processes, irrespective of their mechanisms, and at this more general level there could indeed be a link between reconstruction methods and embryonic development. For our purposes, in fact, what really matters are not the formulae per se, but... 

While comparing formula (6.1) to the Boltzmann formula for a physical system with the identical number of microstates Q, one can easily discover a formal relationship between entropy and information ... 

There is a comprehensive sense in this coincidence (with the accuracy of coefficients) of expressions that derive the quantities of entropy and information The entropy of a system and the information on the system are interrelated. One can consider the information to be identical to that difference between the maximal possible entropy of the system and the entropy actually inherent in the system at the moment of time under con sideration, or vice versa, entropy is identical to the information missing for the full system description. The latter becomes clear after the information on the system has been received. 

Kunz, M. (1986). Entropy and Information Indices of Star Forests. Collect.Czech.CherruComm., 51, 1856-1863. 

Bromaghin, J.F. and R.M. Engeman. 1989. Head to head comparison of SAS and ASTM-proposed probit computer programs. In Acjuatic Toxicology and Environmental Fate, Vol. 11, ASTM STP 1007. G.W. Suter and M.A. Lewis, Eds. American Society for Testing and Materials, Philadelphia, PA, pp. 303-307. Brooks, D.R., J. Collier, B.A. Mauer, J.D.H. Smith, and E.O. Wiley. 1989. Entropy and information in evolving biological systems. Biol. Philos. 4 407—432. 

Dehmer, M. (2008b) Information processing in complex networks graph entropy and information fimctionals. Appl. Math. Computat., 201, 82-94. 

Readers who like a challenging mathematical and physical perspective on the evolution of the universe, with some connection to the entropy and information theme, should try ... 

We can find an apparent association between the Brillouin s relation between entropy and information and the Einstein s relation between mass and energy, which can be exposed through their transferring factors, which is, for the... 

It is not our intention to discuss here the application of theorem (ii) as applied to particular cases known from empirical observations of real processes (see, e.g. [202]) but, instead, we proceed further making use of a well established connection between entropy and information [205]. Accordingly, the information has a character of negative entropy (i.e., we can write / = -q) and therefore, in the old-to-new provisional terminology, we can identity the production of caloric with the destruction of information and the flux of caloric with the information flux in an opposite direction. Theorem (ii) can thus be reformulated in terms of information as... 

J. Wicken Generation of Complexity a thermodynamic and information discussion J. Theoret. Biology 77(1979)349 Entropy and Information suggestion for a common language Phil. Sci. 54 (1987) 176... 

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