Entropy

158 KiB

Open AccessArticle

Entropy Bounds, Holographic Principle and Uncertainty Relation

by M. G. Ivanov and I. V. Volovich

Entropy 2001, 3(2), 66-75; https://doi.org/10.3390/e3020066 - 20 Jun 2001

Cited by 9 | Viewed by 5717

A simple derivation of the bound on entropy is given and the holographic principle is discussed. We estimate the number of quantum states inside space region on the base of uncertainty relation. The result is compared with the Bekenstein formula for entropy bound, which was initially derived from the generalized second law of thermodynamics for black holes. The holographic principle states that the entropy inside a region is bounded by the area of the boundary of that region. This principle can be called the kinematical holographic principle. We argue that it can be derived from the dynamical holographic principle which states that the dynamics of a system in a region should be described by a system which lives on the boundary of the region. This last principle can be valid in general relativity because the ADM hamiltonian reduces to the surface term. Full article

14 KiB

Open AccessMeeting Report

"Information Theory and its Applications to Biology, Finance and Physics" at the Stefan Banach International Mathematical Center (Warsaw, Poland), May 21-26, 2001

by Jonathan D. H. Smith

Entropy 2001, 3(2), 64-65; https://doi.org/10.3390/e3020064 - 11 Jun 2001

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Abstract

The conference was held at the Banach Centre [1] within the European Union Programme Centres of Excellence.[...] Full article

171 KiB

Open AccessArticle

A Cellular Automata Study of Constraints (Dissolvence) in a Percolating Many-Particle System

by Bernard Testa, Lemont B. Kier, Chun-Kao Cheng and Joachim Mayer

Entropy 2001, 3(2), 27-57; https://doi.org/10.3390/e3020027 - 11 Apr 2001

Cited by 2 | Viewed by 7723

Abstract

In a recent study by Kier, Cheng and Testa, simulations were carried out to monitor and quantify the emergence of a collective phenomenon, namely percolation, in a many-particle system modeled by cellular automata (CA). In the present study, the same setup was used to monitor the counterpart to collective behavior, namely the behavior of individual particles, as modeled by occupied cells in the CA simulations. As in the previous study, the input variables were the concentration of occupied cells and their joining and breaking probabilities. The first monitored attribute was the valence configuration (state) of the occupied cells, namely the percent of occupied cells in configuration Fi (%Fi), where i = number of occupied cells joined to that cell. The second monitored attribute was a functional one, namely the probability (in %) of a occupied cell in configuration Fi to move during one iteration (%Mi). First, this study succeeded in quantifying the expected, strong direct influences of the initial conditions on the configuration and movement of occupied cells. Statistical analyses unveiled correlations between initial conditions and cell configurations and movements. In particular, the distribution of configurations (%Fi) varied with concentration with a kinematic-like regularity amenable to mathematical modeling. However, another result also emerged from the work, such that the joining, breaking and concentration factors not only influenced the movement of occupied cells, they also modified each other's influence (Figure 1). These indirect influences have been demonstrated quite clearly, and some partial statistical descriptions were established. Thus, constraints at the level of ingredients (dissolvence) have been characterized as a counterpart to the emergence of a collective behavior (percolation) in very simple CA simulations. Full article

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96 KiB

Open AccessArticle

Maximum Entropy: Clearing up Mysteries

by Marian Grendár, Jr. and Marian Grendár

Entropy 2001, 3(2), 58-63; https://doi.org/10.3390/e3020058 - 08 Apr 2001

Cited by 16 | Viewed by 6653

Abstract

There are several mystifications and a couple of mysteries pertinent to MaxEnt. The mystifications, pitfalls and traps are set up mainly by an unfortunate formulation of Jaynes' die problem, the cause célèbre of MaxEnt. After discussing the mystifications a new formulation of the problem is proposed. Then we turn to the mysteries. An answer to the recurring question 'Just what are we accomplishing when we maximize entropy?' [8], based on MaxProb rationale of MaxEnt [6], is recalled. A brief view on the other mystery: 'What is the relation between MaxEnt and the Bayesian method?' [9], in light of the MaxProb rationale of MaxEnt suggests that there is not and cannot be a conflict between MaxEnt and Bayes Theorem. Full article

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Entropy, Volume 3, Issue 2 (June 2001) – 4 articles , Pages 27-75

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