Naoki Sato
Article: Scientific Élan Vital: Entropy Deficit or Inhomogeneity as a Unified Concept of Driving Forces of Life in Hierarchical Biosphere Driven by Photosynthesis
Entropy 2012, 14(2), 233-251; doi:10.3390/e14020233 - published online 10 February 2012
Show/Hide AbstractAbstract: Life is considered something different from non-living things, but no single driving force can account for all the different aspects of life, which consists of different levels of hierarchy, such as metabolism, cell physiology, multi-cellular development and organization, population dynamics, ecosystem, and evolution. Although free energy is evidently the driving force in biochemical reactions, there is no established relationship between metabolic energy and spatiotemporal organization of living organisms, or between metabolic energy and genetic information. Since Schrödinger pointed out the importance of exporting entropy in maintaining life, misunderstandings of entropy notion have been obstacles in constructing a unified view on the driving forces of life. Here I present a simplified conceptual framework for unifying driving forces of life at various different levels of hierarchy. The key concept is “entropy deficit”, or simply, ‘inhomogeneity’, which is defined as the difference of maximal possible entropy and actual entropy. This is equivalent to information content in genetic information and protein structure, and is also defined similarly for non-homogeneous structures in ecosystems and evolution. Entropy deficit or inhomogeneoity is a unified measure of all driving forces of life, which could be considered a scientific equivalent to ‘élan vital’ of Bergson.

Kevin C. Wolfe and Gregory S. Chirikjian
Article: Quantitative Comparison of Conformational Ensembles
Entropy 2012, 14(2), 213-232; doi:10.3390/e14020213 - published online 10 February 2012
Show/Hide AbstractAbstract: A number of measures have been used in the structural biology literature to compare the shapes or conformations of biological macromolecules. However, the issue of how to compare two ensembles of conformations has received far less attention. Herein, the problem of how to quantitatively compare two such ensembles is addressed in several different ways using concepts from probability and information theory. Ultimately, such metrics could be used in the evaluation of structure-prediction algorithms and the analysis of how conformational mobility is inhibited by bound ligands.

Lena C. Zuchowski
Article: Disentangling Complexity from Randomness and Chaos
Entropy 2012, 14(2), 177-212; doi:10.3390/e14020177 - published online 7 February 2012
Show/Hide AbstractAbstract: This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to neglect the underlying dynamics and to focus exclusively on the phenomenology of complex systems; and linguistic imprecisions in describing these phenomenologies. I will argue that the tendency to discuss phenomenology removed from the underlying dynamics is the main root of the difficulties in distinguishing complex from chaotic or random systems. In my own definition, I will explicitly try to avoid these pitfalls. The theoretical contemplations in this paper will be tested on a sample of five models: the random Kac ring, the chaotic CA30, the regular CA90, the complex CA110 and the complex Bak-Sneppen model. Although these modelling studies are restricted in scope and can only be seen as preliminary, they still constitute on of the first attempts to investigate complex systems comparatively.

Anastasios Anastasiadis
Editorial: Special Issue: Tsallis Entropy
Entropy 2012, 14(2), 174-176; doi:10.3390/e14020174 - published online 3 February 2012
Show/Hide AbstractAbstract: One of the crucial properties of the Boltzmann-Gibbs entropy in the context of classical thermodynamics is extensivity, namely proportionality with the number of elements of the system. The Boltzmann-Gibbs entropy satisfies this prescription if the subsystems are statistically (quasi-) independent, or typically if the correlations within the system are essentially local. In such cases the energy of the system is typically extensive and the entropy is additive. In general, however, the situation is not of this type and correlations may be far from negligible at all scales. Tsallis in 1988 introduced an entropic expression characterized by an index q which leads to a non-extensive statistics. Tsallis entropy, Sq, is the basis of the so called non-extensive statistical mechanics, which generalizes the Boltzmann-Gibbs theory. Tsallis statistics have found applications in a wide range of phenomena in diverse disciplines such as physics, chemistry, biology, medicine, economics, geophysics, etc. The focus of this special issue of Entropy was to solicit contributions that apply Tsallis entropy in various scientific fields. [...]

Suk-Bok Kang , Young-Seuk Cho , Jun-Tae Han and Jinsoo Kim
Article: An Estimation of the Entropy for a Double Exponential Distribution Based on Multiply Type-II Censored Samples
Entropy 2012, 14(2), 161-173; doi:10.3390/e14020161 - published online 31 January 2012
Show/Hide AbstractAbstract: In many life-testing and reliability studies, the experimenter might not always obtain complete information on failure times for all experimental units. Multiply Type-II censored sampling arises in a life-testing experiment whenever the experimenter does not observe the failure times of some units placed on a life-test. In this paper, we obtain estimators for the entropy function of a double exponential distribution under multiply Type-II censored samples using the maximum likelihood estimation and the approximate maximum likelihood estimation procedures. We compare the proposed estimators in the sense of the mean squared errors by using Monte Carlo simulation.

LaVar King Isaacson
Article: Control Parameters for Boundary-Layer Instabilities in Unsteady Shock Interactions
Entropy 2012, 14(2), 131-160; doi:10.3390/e14020131 - published online 31 January 2012
Show/Hide AbstractAbstract: This article presents the computation of a set of control parameters for the deterministic prediction of laminar boundary-layer instabilities induced by an imposed unsteady shock interaction. The objective of the study is exploratory in nature by computing a supersonic flight environment for flow over a blunt body and the deterministic prediction of the spectral entropy rates for the boundary layer subjected to an unsteady pressure disturbance. The deterministic values for the spectral entropy rate within the instabilities are determined for each control parameter. Computational results imply that the instabilities are of a span-wise vortex form, that the maximum vertical velocity wave vector components are produced in the region nearest the wall and that extended transient coherent structures are produced in the boundary layer at a vertical location slightly below the mid-point of the boundary layer.