The Insights of Algorithmic Entropy

Devine, Sean

doi:10.3390/e11010085

Cited by 16 publications

(23 citation statements)

References 47 publications

(88 reference statements)

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“…The relation between the above computer simulation information and the actual information intrinsic to the universe is analogous to the relation between the algorithmic information content (algorithmic entropy or Kolmogorov complexity), the size of the smallest algorithm that can generate a dataset and the actual amount of information contained within that dataset [64,65]. For non-random datasets algorithmic information is always less than the information in the dataset.…”

Section: Algorithmic Information Contentmentioning

confidence: 99%

Holographic Dark Information Energy: Predicted Dark Energy Measurement

Gough

2013

Entropy

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Several models have been proposed to explain the dark energy that is causing universe expansion to accelerate. Here the acceleration predicted by the Holographic Dark Information Energy (HDIE) model is compared to the acceleration that would be produced by a cosmological constant. While identical to a cosmological constant at low redshifts, z < 1, the HDIE model results in smaller Hubble parameter values at higher redshifts, z > 1, reaching a maximum difference of 2.6 ± 0.5% around z ~ 1.7. The next generation of dark energy measurements, both those scheduled to be made in space (ESA's Euclid and NASA's WFIRST missions) and those to be made on the ground (BigBOSS, LSST and Dark Energy Survey), should be capable of determining whether such a difference exists or not. In addition a computer simulation thought experiment is used to show that the algorithmic entropy of the universe always increases because the extra states produced by the accelerating expansion compensate for the loss of entropy from star formation.

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Section: Algorithmic Information Contentmentioning

confidence: 99%

Holographic Dark Information Energy: Predicted Dark Energy Measurement

Gough

2013

Entropy

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“…From this concept, we can introduce the t-time-Kolmogorov Complexity, or t-time-bounded algorithmic entropy [11].…”

Section: Algorithmic Entropymentioning

confidence: 99%

“…The Kolmogorov-Chaitin (KC, by acronym) as new tool possesses many applications, in fields as diverse as Combinatorics, Graph Theory, Analysis of Algorithms, or Learning Theory, among others [10,11].…”

Section: In At Most T(|x|) Steps}mentioning

confidence: 99%

Classifying Entropy Measures

Garrido

2011

Symmetry

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Our paper analyzes some aspects of Uncertainty Measures. We need to obtain new ways to model adequate conditions or restrictions, constructed from vague pieces of information. The classical entropy measure originates from scientific fields; more specifically, from Statistical Physics and Thermodynamics. With time it was adapted by Claude Shannon, creating the current expanding Information Theory. However, the Hungarian mathematician, Alfred Rényi, proves that different and valid entropy measures exist in accordance with the purpose and/or need of application. Accordingly, it is essential to clarify the different types of measures and their mutual relationships. For these reasons, we attempt here to obtain an adequate revision of such fuzzy entropy measures from a mathematical point of view.

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“…Given that there are presently three "traditional understandings of entropy [which] include the thermodynamic approach of Clausius, the statistical mechanics approaches of Boltzmann and Gibbs and the information theory approach of Shannon" [1], it is still difficult to grasp the concept of entropy in an intuitive and straightforward way. It will be shown that connecting Clausius' understanding of entropy with information about mean values in the microscopic world coming out from the statistical approach, an uncomplicated representation of entropy arises, which readily lends itself to be pictorially visualized.…”

Section: Introductionmentioning

confidence: 99%