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Entropy
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Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications
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Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 July 2015) | Viewed by 55014

Special Issue Editors

Dr. Umberto Lucia

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Guest Editor
Dipartimento Energia “Galileo Ferraris”, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Interests: irreversible thermodynamics; quantum thermodynamics; thermodynamics of biosystems; exergoeconomics; econophysics; sustainability
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Giuseppe Grazzini

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Guest Editor
Department of Industrial Engineering, University of Florence, Via S. , Marta 3 - 50139 Firenze, Italy
Interests: thermodynamics, solar energy, thermal conductivity

Special Issue Information

Dear Colleagues,

Applied thermodynamics is the science of both energy and its best use, in relation to the available energy resources. Applied thermodynamics concerns energy and energy transformations, including power production and refrigeration, and the relationships among the properties of matter, including living matter.
The first law of thermodynamics expresses the conservation of the energy, while the second law states that entropy continuously increases for the system and its environment. The second law highlights that energy has quality as well as quantity, and any process occurs with a consequent decrease in this quality.
Nicolas Léonard Sadi Carnot’s study of heat engines revealed the existence of a readily calculable limit for any conversion rate of heat into work. Entropy was introduced by Rudolf Clausius to analyze dissipative processes. Louis Georges Gouy (in 1889) and Aurel Stodola (1905) independently proved that the lost exergy in a process is proportional to the entropy generation. Then, Ilya Prigogine (in 1947) and Hans Ziegler (in 1957) proved, respectively, that a non-equilibrium system develops in a way that attains the minimum entropy production and the maximum entropy production under the present constraints. Moreover, Prigogine extended this approach to complex systems in physics, chemistry, and biology.
In 1982, Adrian Bejan introduced the minimum entropy generation approach, which is an optimization method for engineers’ designs. Then, he developed an improvement, named the constructal law, which is particularly effective for explaining the optimal shapes of natural structures.
All these approaches allow us to highlight the need for a unified thermodynamic approach to complex system evolution, based on the analysis of the interaction between systems and environment, by considering the flows across the system's border.

Prof. Giuseppe Grazzini
Dr. Umberto Lucia
Guest Editors

Manuscript Submission Information

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Keywords

  • entropy generation
  • irreversibility
  • open systems
  • complex systems
  • constructal theory
  • maximum entropy generation
  • minimum entropy generation
  • second law analysis
  • quantum thermodynamics
  • non-conventional application of the second law

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Published Papers (7 papers)

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Research

3410 KiB  
Article
Comparing the Models of Steepest Entropy Ascent Quantum Thermodynamics, Master Equation and the Difference Equation for a Simple Quantum System Interacting with Reservoirs
by Charles E. Smith
Entropy 2016, 18(5), 176; https://doi.org/10.3390/e18050176 - 12 May 2016
Cited by 7 | Viewed by 4795
Abstract
There is increasing interest concerning the details about how quantum systems interact with their surroundings. A number of methodologies have been used to describe these interactions, including Master Equations (ME) based on a system-plus-reservoir (S + R) approach, and more recently, Steepest Entropy [...] Read more.
There is increasing interest concerning the details about how quantum systems interact with their surroundings. A number of methodologies have been used to describe these interactions, including Master Equations (ME) based on a system-plus-reservoir (S + R) approach, and more recently, Steepest Entropy Ascent Quantum Thermodynamics (SEAQT) which asserts that entropy is a fundamental physical property and that isolated quantum systems that are not at stable equilibrium may spontaneously relax without environmental influences. In this paper, the ME, SEAQT approaches, and a simple linear difference equation (DE) model are compared with each other and experimental data in order to study the behavior of a single trapped ion as it interacts with one or more external heat reservoirs. The comparisons of the models present opportunities for additional study to verify the validity and limitations of these approaches. Full article
(This article belongs to the Special Issue Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications)
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762 KiB  
Article
Entropy Production in the Theory of Heat Conduction in Solids
by Federico Zullo
Entropy 2016, 18(3), 87; https://doi.org/10.3390/e18030087 - 8 Mar 2016
Cited by 14 | Viewed by 6586
Abstract
The evolution of the entropy production in solids due to heat transfer is usually associated with the Prigogine’s minimum entropy production principle. In this paper, we propose a critical review of the results of Prigogine and some comments on the succeeding literature. We [...] Read more.
The evolution of the entropy production in solids due to heat transfer is usually associated with the Prigogine’s minimum entropy production principle. In this paper, we propose a critical review of the results of Prigogine and some comments on the succeeding literature. We suggest a characterization of the evolution of the entropy production of the system through the generalized Fourier modes, showing that they are the only states with a time independent entropy production. The variational approach and a Lyapunov functional of the temperature, monotonically decreasing with time, are discussed. We describe the analytic properties of the entropy production as a function of time in terms of the generalized Fourier coefficients of the system. Analytical tools are used throughout the paper and numerical examples will support the statements. Full article
(This article belongs to the Special Issue Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications)
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3153 KiB  
Article
Numerical Study of Entropy Generation Within Thermoacoustic Heat Exchangers with Plane Fins
by Antonio Piccolo
Entropy 2015, 17(12), 8228-8239; https://doi.org/10.3390/e17127875 - 16 Dec 2015
Cited by 9 | Viewed by 5070
Abstract
In this paper a simplified two-dimensional computational model for studying the entropy generation characteristics of thermoacoustic heat exchangers with plane fins is presented. The model integrates the equations of the standard linear thermoacoustic theory into an energy balance-based numerical calculus scheme. Relevant computation [...] Read more.
In this paper a simplified two-dimensional computational model for studying the entropy generation characteristics of thermoacoustic heat exchangers with plane fins is presented. The model integrates the equations of the standard linear thermoacoustic theory into an energy balance-based numerical calculus scheme. Relevant computation results are the spatial distribution of the time-averaged temperature, heat fluxes and entropy generation rates within a channel of a parallel-plate stack and adjoining heat exchangers. For a thermoacoustic device working in the refrigeration mode, this study evidences as a target refrigeration output level can be achieved selecting simultaneously the heat exchangers fin length and fin interspacing for minimum entropy generation and that the resulting configuration is a point of maximum coefficient of performance. The proposed methodology, when extended to other configurations, could be used as a viable design tool for heat exchangers in thermoacoustic applications. Full article
(This article belongs to the Special Issue Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications)
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5093 KiB  
Article
A Robust Image Tampering Detection Method Based on Maximum Entropy Criteria
by Bo Zhao, Guihe Qin and Pingping Liu
Entropy 2015, 17(12), 7948-7966; https://doi.org/10.3390/e17127854 - 1 Dec 2015
Cited by 6 | Viewed by 5721
Abstract
This paper proposes a novel image watermarking method based on local energy and maximum entropy aiming to improve the robustness. First, the image feature distribution is extracted by employing the local energy model and then it is transformed as a digital watermark by [...] Read more.
This paper proposes a novel image watermarking method based on local energy and maximum entropy aiming to improve the robustness. First, the image feature distribution is extracted by employing the local energy model and then it is transformed as a digital watermark by employing a Discrete Cosine Transform (DCT). An offset image is thus obtained according to the difference between the extracted digital watermarking and the feature distribution of the watermarked image. The entropy of the pixel value distribution is computed first. The Lorenz curve is used to measure the polarization degree of the pixel value distribution. In the pixel location distribution flow, the maximum entropy criteria is applied in segmenting the offset image into potentially tampered regions and unchanged regions. All-connected graph and 2-D Gaussian probability are utilized to obtain the probability distribution of the pixel location. Finally, the factitious tampering probability value of a pending detected image is computed through combining the weighting factors of pixel value and pixel location distribution. Experimental results show that the proposed method is more robust against the commonly used image processing operations, such as Gaussian noise, impulse noise, etc. Simultaneously, the proposed method achieves high sensitivity against factitious tampering. Full article
(This article belongs to the Special Issue Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications)
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747 KiB  
Article
The Second Law Today: Using Maximum-Minimum Entropy Generation
by Umberto Lucia and Giuseppe Grazzini
Entropy 2015, 17(11), 7786-7797; https://doi.org/10.3390/e17117786 - 20 Nov 2015
Cited by 9 | Viewed by 5839
Abstract
There are a great number of thermodynamic schools, independent of each other, and without a powerful general approach, but with a split on non-equilibrium thermodynamics. In 1912, in relation to the stationary non-equilibrium states, Ehrenfest introduced the fundamental question on the existence of [...] Read more.
There are a great number of thermodynamic schools, independent of each other, and without a powerful general approach, but with a split on non-equilibrium thermodynamics. In 1912, in relation to the stationary non-equilibrium states, Ehrenfest introduced the fundamental question on the existence of a functional that achieves its extreme value for stable states, as entropy does for the stationary states in equilibrium thermodynamics. Today, the new branch frontiers of science and engineering, from power engineering to environmental sciences, from chaos to complex systems, from life sciences to nanosciences, etc. require a unified approach in order to optimize results and obtain a powerful approach to non-equilibrium thermodynamics and open systems. In this paper, a generalization of the Gouy–Stodola approach is suggested as a possible answer to the Ehrenfest question. Full article
(This article belongs to the Special Issue Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications)
850 KiB  
Article
Life’s a Gas: A Thermodynamic Theory of Biological Evolution
by Keith R. Skene
Entropy 2015, 17(8), 5522-5548; https://doi.org/10.3390/e17085522 - 31 Jul 2015
Cited by 41 | Viewed by 18330
Abstract
This paper outlines a thermodynamic theory of biological evolution. Beginning with a brief summary of the parallel histories of the modern evolutionary synthesis and thermodynamics, we use four physical laws and processes (the first and second laws of thermodynamics, diffusion and the maximum [...] Read more.
This paper outlines a thermodynamic theory of biological evolution. Beginning with a brief summary of the parallel histories of the modern evolutionary synthesis and thermodynamics, we use four physical laws and processes (the first and second laws of thermodynamics, diffusion and the maximum entropy production principle) to frame the theory. Given that open systems such as ecosystems will move towards maximizing dispersal of energy, we expect biological diversity to increase towards a level, Dmax, representing maximum entropic production (Smax). Based on this theory, we develop a mathematical model to predict diversity over the last 500 million years. This model combines diversification, post-extinction recovery and likelihood of discovery of the fossil record. We compare the output of this model with that of the observed fossil record. The model predicts that life diffuses into available energetic space (ecospace) towards a dynamic equilibrium, driven by increasing entropy within the genetic material. This dynamic equilibrium is punctured by extinction events, which are followed by restoration of Dmax through diffusion into available ecospace. Finally we compare and contrast our thermodynamic theory with the MES in relation to a number of important characteristics of evolution (progress, evolutionary tempo, form versus function, biosphere architecture, competition and fitness). Full article
(This article belongs to the Special Issue Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications)
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1758 KiB  
Article
Entropy Production of Stars
by Leonid M. Martyushev and Sergey N. Zubarev
Entropy 2015, 17(6), 3645-3655; https://doi.org/10.3390/e17063645 - 2 Jun 2015
Cited by 3 | Viewed by 6932
Abstract
The entropy production (inside the volume bounded by a photosphere) of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume) entropy [...] Read more.
The entropy production (inside the volume bounded by a photosphere) of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume) entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude) is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production. Full article
(This article belongs to the Special Issue Maximum versus Minimum Entropy Generation: Theoretical Developments and Applications)
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