Vladimir Hnizdo and Michael K. Gilson
Article: Thermodynamic and Differential Entropy under a Change of Variables
Entropy 2010, 12(3), 578-590; doi:10.3390/e12030578 - published online 16 March 2010
Show/Hide AbstractAbstract: The differential Shannon entropy of information theory can change under a change of variables (coordinates), but the thermodynamic entropy of a physical system must be invariant under such a change. This difference is puzzling, because the Shannon and Gibbs entropies have the same functional form. We show that a canonical change of variables can, indeed, alter the spatial component of the thermodynamic entropy just as it alters the differential Shannon entropy. However, there is also a momentum part of the entropy, which turns out to undergo an equal and opposite change when the coordinates are transformed, so that the total thermodynamic entropy remains invariant. We furthermore show how one may correctly write the change in total entropy for an isothermal physical process in any set of spatial coordinates.

Claudio Fontanesi
Article: Entropy Variation in the Two-dimensional Phase Transition of Anthracene Adsorbed at the Hg Electrode/Ethylene Glycol Solution Interface
Entropy 2010, 12(3), 570-577; doi:10.3390/e12030570 - published online 16 March 2010
Show/Hide AbstractAbstract: The adsorption of anthracene (C₁₄H₁₀), at the mercury electrode/ethylene glycol (EG) solution interface, is characterized by a low and almost constant capacity (about 8 μF cm⁻²) region (capacitive “pit” or “plateau”) in capacity vs. potential curves, upon selection of suitable values of temperature, bulk concentration and applied potential values. This result is rationalized assuming the occurrence of a 2D phase transition between two distinct adsorbed phases: (i) a “disordered” phase, characterized by a flat “parallel” disposition of the aromatic moiety on the electrode surface (ii) an “ordered” phase, characterized by a “perpendicular” disposition of the aromatic moiety on the electrode surface. The experimental evidence is rationalized by considering the chemical potential as an explicit function of the “electric field/adsorbed molecule” interaction. Such a modelistic approach enables the determination of the relevant standard entropy variation.

Eugene Kagan
Article: Turing Systems, Entropy, and Kinetic Models for Self-Healing Surfaces
Entropy 2010, 12(3), 554-569; doi:10.3390/e12030554 - published online 15 March 2010
Show/Hide AbstractAbstract: The paper addresses the methods of description of friction-induced self-healing at the interface between two solid bodies. A macroscopic description of self-healing is based on a Turing system for the transfer of matter that leads to self-organization at the interface in the case of an unstable state. A microscopic description deals with a kinetic model of the process and entropy production during self-organization. The paper provides a brief overview of the Turing system approach and statistical kinetic models. The relation between these methods and the description of the self-healing surfaces is discussed, as well as results of their application. The analytical considerations are illustrated by numerical simulations.

Inna Semetsky
Article: Information and Signs: The Language of Images
Entropy 2010, 12(3), 528-553; doi:10.3390/e12030528 - published online 12 March 2010
Show/Hide AbstractAbstract: Since time immemorial, philosophers and scientists were searching for a “machine code” of the so-called Mentalese language capable of processing information at the pre-verbal, pre-expressive level. In this paper I suggest that human languages are only secondary to the system of primitive extra-linguistic signs which are hardwired in humans and serve as tools for understanding selves and others; and creating meanings for the multiplicity of experiences. The combinatorial semantics of the Mentalese may find its unorthodox expression in the semiotic system of Tarot images, the latter serving as the ”keys” to the encoded proto-mental information. The paper uses some works in systems theory by Erich Jantsch and Erwin Laszlo and relates Tarot images to the archetypes of the field of collective unconscious posited by Carl Jung. Our subconscious beliefs, hopes, fears and desires, of which we may be unaware at the subjective level, do have an objective compositional structure that may be laid down in front of our eyes in the format of pictorial semiotics representing the universe of affects, thoughts, and actions. Constructing imaginative narratives based on the expressive “language” of Tarot images enables us to anticipate possible consequences and consider a range of future options. The thesis advanced in this paper is also supported by the concept of informational universe of contemporary cosmology.

Esteban Fernández-Vázquez
Article: Recovering Matrices of Economic Flows from Incomplete Data and a Composite Prior
Entropy 2010, 12(3), 516-527; doi:10.3390/e12030516 - published online 12 March 2010
Show/Hide AbstractAbstract: In several socioeconomic applications, matrices containing information on flows-trade, income or migration flows, for example–are usually not constructed from direct observation but are rather estimated, since the compilation of the information required is often extremely expensive and time-consuming. The estimation process takes as point of departure another matrix which is adjusted until it optimizes some divergence criterion and simultaneously is consistent with some partial information-row and column margins–of the target matrix. Among all the possible criteria to be considered, one of the most popular is the Kullback-Leibler divergence [1], leading to the well-known Cross-Entropy technique. This paper proposes the use of a composite Cross-Entropy approach that allows for introducing a mixture of two types of a priori information–two possible matrices to be included as point of departure in the estimation process. By means of a Monte Carlo simulation experiment, we will show that under some circumstances this approach outperforms other competing estimators. Besides, a real-world case with a matrix of interregional trade is included to show the applicability of the suggested technique.

Jesper Haglund, Fredrik Jeppsson and Helge Strömdahl
Article: Different Senses of Entropy—Implications for Education
Entropy 2010, 12(3), 490-515; doi:10.3390/e12030490 - published online 12 March 2010
Show/Hide AbstractAbstract: A challenge in the teaching of entropy is that the word has several different senses, which may provide an obstacle for communication. This study identifies five distinct senses of the word ‘entropy’, using the Principled Polysemy approach from the field of linguistics. A semantic network is developed of how the senses are related, using text excerpts from dictionaries, text books and text corpora. Educational challenges such as the existence of several formal senses of entropy and the intermediary position of entropy as disorder along the formal/non-formal scale are presented using a two-Dimensional Semiotic/semantic Analysing Schema (2-D SAS).