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Entropy, Volume 13, Issue 2 (February 2011), Pages 293-569

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Research

Jump to: Review

Open AccessArticle A Maximum Entropy Modelling of the Rain Drop Size Distribution
Entropy 2011, 13(2), 293-315; doi:10.3390/e13020293
Received: 30 December 2010 / Revised: 13 January 2011 / Accepted: 20 January 2011 / Published: 26 January 2011
Cited by 3 | PDF Full-text (450 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents a maximum entropy approach to Rain Drop Size Distribution (RDSD) modelling. It is shown that this approach allows (1) to use a physically consistent rationale to select a particular probability density function (pdf) (2) to provide an alternative method for
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This paper presents a maximum entropy approach to Rain Drop Size Distribution (RDSD) modelling. It is shown that this approach allows (1) to use a physically consistent rationale to select a particular probability density function (pdf) (2) to provide an alternative method for parameter estimation based on expectations of the population instead of sample moments and (3) to develop a progressive method of modelling by updating the pdf as new empirical information becomes available. The method is illustrated with both synthetic and real RDSD data, the latest coming from a laser disdrometer network specifically designed to measure the spatial variability of the RDSD. Full article
(This article belongs to the Special Issue Advances in Statistical Mechanics)
Open AccessArticle Spin-Currents and Spin-Pumping Forces for Spintronics
Entropy 2011, 13(2), 316-331; doi:10.3390/e13020316
Received: 9 December 2010 / Revised: 24 December 2010 / Accepted: 28 December 2010 / Published: 28 January 2011
Cited by 8 | PDF Full-text (158 KB) | HTML Full-text | XML Full-text
Abstract
A general definition of the Spintronics concept of spin-pumping is proposed as generalized forces conjugated to the spin degrees of freedom in the framework of the theory of mesoscopic non-equilibrium thermodynamics. It is shown that at least three different kinds of spin-pumping forces
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A general definition of the Spintronics concept of spin-pumping is proposed as generalized forces conjugated to the spin degrees of freedom in the framework of the theory of mesoscopic non-equilibrium thermodynamics. It is shown that at least three different kinds of spin-pumping forces and associated spin-currents can be defined in the most simple spintronics system: the Ferromagnetic/Non-Ferromagnetic metal interface. Furthermore, the generalized force associated with the ferromagnetic collective variable is also introduced on an equal footing to describe the coexistence of the spin of the conduction electrons (paramagnetic spins attached to s-band electrons) and the ferromagnetic-order parameter. The dynamical coupling between these two kinds of magnetic degrees of freedom is presented and interpreted in terms of spin-transfer effects. Full article
(This article belongs to the Special Issue Advances in Thermodynamics)
Open AccessArticle Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation
Entropy 2011, 13(2), 332-366; doi:10.3390/e13020332
Received: 12 January 2011 / Revised: 25 January 2011 / Accepted: 25 January 2011 / Published: 31 January 2011
Cited by 1 | PDF Full-text (227 KB)
Abstract
The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the
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The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the free energy and the potential of dissipation. In the framework of standard generalized materials the internal state evolution is governed by a variational inequality which depends on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated to the dissipative process. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and for damaged materials. Full article
(This article belongs to the Special Issue Advances in Thermodynamics)
Open AccessArticle Lagrange Equations Coupled to a Thermal Equation: Mechanics as Consequence of Thermodynamics
Entropy 2011, 13(2), 367-378; doi:10.3390/e13020367
Received: 23 December 2010 / Revised: 19 January 2011 / Accepted: 20 January 2011 / Published: 31 January 2011
Cited by 1 | PDF Full-text (115 KB) | HTML Full-text | XML Full-text
Abstract
Following the analytic approach to thermodynamics developed by Stückelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the
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Following the analytic approach to thermodynamics developed by Stückelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction term. Finally, we apply our coupled evolution equations to study the thermodynamics of an isolated system consisting of identical point particles interacting through a harmonic potential. Full article
(This article belongs to the Special Issue Advances in Thermodynamics)
Open AccessArticle Recent Progresses in Characterising Information Inequalities
Entropy 2011, 13(2), 379-401; doi:10.3390/e13020379
Received: 1 December 2010 / Revised: 19 January 2011 / Accepted: 28 January 2011 / Published: 31 January 2011
Cited by 17 | PDF Full-text (174 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalities,
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In this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalities, followed by the first non-Shannon inequality proved by Zhang et al. in 1998 [1]. The discovery of this non-Shannon inequality is a breakthrough in the area and has led to the subsequent discovery of many more non-Shannon inequalities. We will also review the close relations between information inequalities and other research areas such as Kolmogorov complexity, determinantal inequalities, and group-theoretic inequalities. These relations have led to non-traditional techniques in proving information inequalities and at the same time made impacts back onthose related areas by the introduction of information-theoretic tools. Full article
Open AccessArticle Deterministic Prediction of the Entropy Increase in a Sudden Expansion
Entropy 2011, 13(2), 402-421; doi:10.3390/e13020402
Received: 24 December 2010 / Revised: 25 January 2011 / Accepted: 25 January 2011 / Published: 31 January 2011
Cited by 5 | PDF Full-text (376 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents the results of a study of the prediction of the entropy growth within an internal free shear layer of an ideal gas flow downstream of a sudden expansion of the flow area. The objective of the study is exploratory in
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This paper presents the results of a study of the prediction of the entropy growth within an internal free shear layer of an ideal gas flow downstream of a sudden expansion of the flow area. The objective of the study is exploratory in nature by invoking concepts from information theory to connect the deterministic prediction of the spectral entropy growth within the shear layer to the experimentally inferred increase in entropy across the flow region. The deterministic prediction of the spectral entropy increase along the shear layer is brought into agreement with the experimentally inferred increase in entropy through the ad hoc inclusion of the activation spectral entropy. The values for this activation spectral entropy are directly related to the area ratios across the expansion region and have a specific numerical value for each area ratio. Full article
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Open AccessArticle On the Dynamic Robustness of a Non-Endoreversible Engine Working in Different Operation Regimes
Entropy 2011, 13(2), 422-436; doi:10.3390/e13020422
Received: 29 December 2010 / Revised: 17 January 2011 / Accepted: 20 January 2011 / Published: 8 February 2011
Cited by 2 | PDF Full-text (317 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we focused mainly in the analysis of stability of a non-endoreversible Curzon-Ahlborn engine working in an ecological regime. For comparison purposes we also include the Maximum Efficient Power (MEP) regime taking into account the engine time delays. When the system’s
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In this work, we focused mainly in the analysis of stability of a non-endoreversible Curzon-Ahlborn engine working in an ecological regime. For comparison purposes we also include the Maximum Efficient Power (MEP) regime taking into account the engine time delays. When the system’s dynamic stability is compared with its thermodynamics properties (efficiency and power output), we find that the temperature ratio τ = T1/T2 represents a trade-off between stability and energetic properties. When we take the non-endoreversible case, τ can increases to values greater than R (where R is the non-endoreversible parameter) but not greater than one. We reformulate an important difference between this case and the other two, Maximum Power (MP) and MEP regime, in which τ = R. Finally, we demonstrated that the total time delay does not destabilize the steady state of system. It does not seem to play a role in the dynamic thermodynamic property trade-off. Full article
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Open AccessArticle The Entropy of Progressively Censored Samples
Entropy 2011, 13(2), 437-449; doi:10.3390/e13020437
Received: 21 December 2010 / Revised: 7 January 2011 / Accepted: 8 January 2011 / Published: 9 February 2011
Cited by 8 | PDF Full-text (125 KB) | HTML Full-text | XML Full-text
Abstract
In many life-testing and reliability studies, the experimenter might not always obtain complete information on failure times for all experimental units. Among the different censoring schemes, the progressive censoring scheme has received a considerable attention in the last few years. The aim of
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In many life-testing and reliability studies, the experimenter might not always obtain complete information on failure times for all experimental units. Among the different censoring schemes, the progressive censoring scheme has received a considerable attention in the last few years. The aim of this paper is simplifying the entropy of progressively Type II censored samples. We propose an indirect approach using a decomposition of the entropy in progressively Type II censored samples to simplify the calculation. Some recurrence relations for the entropy in progressively Type II censored samples are derived to facilitate this calculation. An efficient computational method is derived that simplifies computation of the entropy in progressively Type II censored samples to a sum; entropy in collections order statistics. We compute the entropy in a collection of progressively Type II censored samples for some known distributions. Full article
Open AccessArticle Information Theoretic Hierarchical Clustering
Entropy 2011, 13(2), 450-465; doi:10.3390/e13020450
Received: 8 December 2010 / Revised: 31 December 2010 / Accepted: 27 January 2011 / Published: 10 February 2011
Cited by 6 | PDF Full-text (298 KB) | HTML Full-text | XML Full-text
Abstract
Hierarchical clustering has been extensively used in practice, where clusters can be assigned and analyzed simultaneously, especially when estimating the number of clusters is challenging. However, due to the conventional proximity measures recruited in these algorithms, they are only capable of detecting mass-shape
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Hierarchical clustering has been extensively used in practice, where clusters can be assigned and analyzed simultaneously, especially when estimating the number of clusters is challenging. However, due to the conventional proximity measures recruited in these algorithms, they are only capable of detecting mass-shape clusters and encounter problems in identifying complex data structures. Here, we introduce two bottom-up hierarchical approaches that exploit an information theoretic proximity measure to explore the nonlinear boundaries between clusters and extract data structures further than the second order statistics. Experimental results on both artificial and real datasets demonstrate the superiority of the proposed algorithm compared to conventional and information theoretic clustering algorithms reported in the literature, especially in detecting the true number of clusters. Full article
(This article belongs to the Special Issue Advances in Information Theory)
Open AccessArticle Estimating Neuronal Information: Logarithmic Binning of Neuronal Inter-Spike Intervals
Entropy 2011, 13(2), 485-501; doi:10.3390/e13020485
Received: 9 December 2010 / Revised: 14 January 2011 / Accepted: 26 January 2011 / Published: 10 February 2011
Cited by 6 | PDF Full-text (143 KB) | HTML Full-text | XML Full-text
Abstract
Neurons communicate via the relative timing of all-or-none biophysical signals called spikes. For statistical analysis, the time between spikes can be accumulated into inter-spike interval histograms. Information theoretic measures have been estimated from these histograms to assess how information varies across organisms, neural
[...] Read more.
Neurons communicate via the relative timing of all-or-none biophysical signals called spikes. For statistical analysis, the time between spikes can be accumulated into inter-spike interval histograms. Information theoretic measures have been estimated from these histograms to assess how information varies across organisms, neural systems, and disease conditions. Because neurons are computational units that, to the extent they process time, work not by discrete clock ticks but by the exponential decays of numerous intrinsic variables, we propose that neuronal information measures scale more naturally with the logarithm of time. For the types of inter-spike interval distributions that best describe neuronal activity, the logarithm of time enables fewer bins to capture the salient features of the distributions. Thus, discretizing the logarithm of inter-spike intervals, as compared to the inter-spike intervals themselves, yields histograms that enable more accurate entropy and information estimates for fewer bins and less data. Additionally, as distribution parameters vary, the entropy and information calculated from the logarithm of the inter-spike intervals are substantially better behaved, e.g., entropy is independent of mean rate, and information is equally affected by rate gains and divisions. Thus, when compiling neuronal data for subsequent information analysis, the logarithm of the inter-spike intervals is preferred, over the untransformed inter-spike intervals, because it yields better information estimates and is likely more similar to the construction used by nature herself. Full article
(This article belongs to the Special Issue Advances in Information Theory)
Open AccessArticle Microcanonical Description of (Micro) Black Holes
Entropy 2011, 13(2), 502-517; doi:10.3390/e13020502
Received: 12 January 2011 / Revised: 27 January 2011 / Accepted: 8 February 2011 / Published: 14 February 2011
Cited by 14 | PDF Full-text (139 KB) | HTML Full-text | XML Full-text
Abstract
The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g., negative specific heat (not allowed in the canonical ensemble) and loss of unitarity,
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The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g., negative specific heat (not allowed in the canonical ensemble) and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existenceis predicted in models with extra-spatial dimensions. Full article
(This article belongs to the Special Issue Entropy in Quantum Gravity)
Open AccessArticle Entangled States in Quantum Cosmology and the Interpretation of Λ
Entropy 2011, 13(2), 528-541; doi:10.3390/e13020528
Received: 13 December 2010 / Revised: 2 February 2011 / Accepted: 16 February 2011 / Published: 17 February 2011
Cited by 6 | PDF Full-text (125 KB) | HTML Full-text | XML Full-text
Abstract
The cosmological constant Λ can be achieved as the result of entangled and statistically correlated minisuperspace cosmological states, built up by using a minimal choice of observable quantities, i.e., Ωm and Ωk, which assign the cosmic dynamics. In particular, we consider a cosmological
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The cosmological constant Λ can be achieved as the result of entangled and statistically correlated minisuperspace cosmological states, built up by using a minimal choice of observable quantities, i.e., Ωm and Ωk, which assign the cosmic dynamics. In particular, we consider a cosmological model where two regions, corresponding to two correlated eras, are involved; the present universe description would be, in this way, given by a density matrix ˆρ, corresponding to an entangled final state. Starting from this assumption, it is possible to infer some considerations on the cosmic thermodynamics by evaluating the Von Neumann entropy. The correlation between different regions by the entanglement phenomenon results in the existence of Λ (in particular ΩΛ) which could be interpreted in the framework of the recent astrophysical observations. As a byproduct, this approach could provide a natural way to solve the so called coincidence problem. Full article
(This article belongs to the Special Issue Entropy in Quantum Gravity)
Open AccessArticle Size Effects on the Entropy Production in Oscillatory Flow between Parallel Plates
Entropy 2011, 13(2), 542-553; doi:10.3390/e13020542
Received: 1 January 2011 / Revised: 27 January 2011 / Accepted: 11 February 2011 / Published: 18 February 2011
Cited by 2 | PDF Full-text (148 KB) | HTML Full-text | XML Full-text
Abstract
The heat transfer problem of a zero-mean oscillatory flow of a Maxwell fluid between infinite parallel plates with boundary conditions of the third kind is considered. The local and global time-averaged entropy production are computed, and the consequences of convective cooling of the
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The heat transfer problem of a zero-mean oscillatory flow of a Maxwell fluid between infinite parallel plates with boundary conditions of the third kind is considered. The local and global time-averaged entropy production are computed, and the consequences of convective cooling of the plates are also assessed. It is found that the global entropy production is a minimum for certain suitable combination of the physical parameters and a discrete set of values of the separation between the parallel plates. The transferred heat at the plates also shows minima in the same discrete set of values of the plates separation. Full article
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Open AccessArticle Amines in the Earth’s Atmosphere: A Density Functional Theory Study of the Thermochemistry of Pre-Nucleation Clusters
Entropy 2011, 13(2), 554-569; doi:10.3390/e13020554
Received: 1 January 2011 / Revised: 11 January 2011 / Accepted: 27 January 2011 / Published: 21 February 2011
Cited by 68 | PDF Full-text (2153 KB) | HTML Full-text | XML Full-text
Abstract
The impact of organic species which are present in the Earth’s atmosphere on the burst of new particles is critically important for the understanding of the molecular nature of atmospheric nucleation phenomena. Amines have recently been proposedas possible stabilizers of binary pre-nucleation
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The impact of organic species which are present in the Earth’s atmosphere on the burst of new particles is critically important for the understanding of the molecular nature of atmospheric nucleation phenomena. Amines have recently been proposed as possible stabilizers of binary pre-nucleation clusters. In order to advance the understanding of atmospheric nucleation phenomena, a quantum-chemical study of hydrogen-bonded complexes of binary sulfuric acid-water clusters with methyl-, dimethyl- and trimethylamines representing common atmospheric organic species, vegetation products and laboratory impurities has been carried out. The thermochemical stability of the sulfuric acid-amines-water complexes was found to be higher than that of the sulfuric acid-ammonia-water complexes, in qualitative agreement with the previous studies. However, the enhancement in stability due to amines appears to not be large enough to overcome the difference in typical atmospheric concentrations of ammonia and amines. Further research is needed in order to address the existing uncertainties and to reach a final conclusion about the importance of amines for the atmospheric nucleation. Full article
(This article belongs to the Special Issue Advances in Thermodynamics)
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Review

Jump to: Research

Open AccessReview Primitive Membrane Formation, Characteristics and Roles in the Emergent Properties of a Protocell
Entropy 2011, 13(2), 466-484; doi:10.3390/e13020466
Received: 23 December 2010 / Revised: 13 January 2011 / Accepted: 24 January 2011 / Published: 10 February 2011
Cited by 8 | PDF Full-text (352 KB) | HTML Full-text | XML Full-text
Abstract
All contemporary living cells are composed of a collection of self-assembled molecular elements that by themselves are non-living but through the creation of a network exhibit the emergent properties of self-maintenance, self-reproduction, and evolution. This short review deals with the on-going research that
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All contemporary living cells are composed of a collection of self-assembled molecular elements that by themselves are non-living but through the creation of a network exhibit the emergent properties of self-maintenance, self-reproduction, and evolution. This short review deals with the on-going research that aims at either understanding how life emerged on the early Earth or creating artificial cells assembled from a collection of small chemicals. In particular, this article focuses on the work carried out to investigate how self-assembled compartments, such as amphiphile and lipid vesicles, contribute to the emergent properties as part of a greater system. Full article
(This article belongs to the Special Issue Emergence in Chemical Systems)
Open AccessReview The Nature of Stability in Replicating Systems
Entropy 2011, 13(2), 518-527; doi:10.3390/e13020518
Received: 14 December 2010 / Revised: 14 January 2011 / Accepted: 10 February 2011 / Published: 15 February 2011
Cited by 4 | PDF Full-text (134 KB) | HTML Full-text | XML Full-text
Abstract
We review the concept of dynamic kinetic stability, a type of stability associated specifically with replicating entities, and show how it differs from the well-known and established (static) kinetic and thermodynamic stabilities associated with regular chemical systems. In the process we demonstrate how
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We review the concept of dynamic kinetic stability, a type of stability associated specifically with replicating entities, and show how it differs from the well-known and established (static) kinetic and thermodynamic stabilities associated with regular chemical systems. In the process we demonstrate how the concept can help bridge the conceptual chasm that continues to separate the physical and biological sciences by relating the nature of stability in the animate and inanimate worlds, and by providing additional insights into the physicochemical nature of abiogenesis. Full article
(This article belongs to the Special Issue Emergence in Chemical Systems)
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