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Entropy of Complex Processes and Systems - 1st Edition - ISBN: 9780128216620, 9780128225394

Entropy of Complex Processes and Systems

1st Edition

Author: Eugene Barsky
Paperback ISBN: 9780128216620
eBook ISBN: 9780128225394
Imprint: Elsevier
Published Date: 22nd July 2020
Page Count: 308
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Entropy of Complex Processes and Systems formalizes our understanding of many complex processes, including the development of the methodology of analytical computation of complex processes as applied in many industries, such as ore processing, or more generally, in areas of natural sciences. The adequacy of the results of these calculations is confirmed by numerous experimental data obtained both on pilots and industrial facilities. The book also provides a thorough analysis of the underlying physical foundations of entropy performed from new standpoints that are of interest to theoreticians studying contemporary expositions.

Key Features

  • Provides methodologies for controlling and optimizing complex processes in branches of industry that involve transformation of materials or substances
  • Describes entropy as the universal characteristic of a stochastic process independent of the system
  • Introduces a new definition of entropy specifically related to dynamical phenomena


Scientists and students in (chemical) engineering sciences dealing with mass random processes and systems. Engineers in chemical technology working in industry dealing with the optimization of complex industrial processes

Table of Contents

1. Brief history, properties and problems of the entropy parameter
1.1. Thermodynamic entropy
1.2. Statistical substantiation of entropy
1.3. Substantiation of the statistical analysis validity
1.4. Some problematic aspects of entropy
1.5. Gibbs paradox and problems of gaseous systems separation
1.6. Actual separation of gases
1.7. Solution of the Gibbs’ paradox
1.8. Phenomenological problems of the second law
a. Essence of the problem
b. Thermodynamic aspects of biological systems 

2. Statistical component of entropy
2.1. Notions of randomness, chaos and stability
2.2. Probabilistic characteristics
2.3. Random values and distribution functions
2.4. Probabilistic interpretation of granulometric characteristics of a poly-fractional mixture of solid particles
2.5. Determination of average values of random quantities
2.6. Possibility of single-valued evaluation of complicated compositions of various systems
2.7.  Uncertainty of mixture composition
2.8.  Separation efficiency
2.9. Separation optimality condition according to the entropic criterion for binary mixtures
2.10.  Objective evaluation of multi-component systems separation 
2.11. Example of optimization of separation into four components
2.12.  Mathematical model of separation into n components
2.13. Unambiguous evaluation of the completeness of a complicated object in the process of building
2.14. Unambiguous evaluation of complex treatment of natural resources

3. Dynamic component of entropy
3.1. Modeling and analogy – bases of comprehending dynamic systems
3.2. Justification of physical analogy
3.3. Justification of statistical model of two-phase flows in critical regimes
3.4. Determination of distribution parameters
3.5. Justification of entropy parameter of two-phase flows
3.6. Main properties of dynamic entropy characterizing a two-phase flow
3.7. Steady state as a condition of entropy maximality
3.8. Regarding the formation of the parameter of a dynamic system entropy
3.9.  Entropy and probability distribution
3.10. Multi-dimensional statistical model of a two-phase flow
3.11. Mobility of a two-phase flow
3.12. Other invariants for a two-phase flow
3.13. Canonical distributions in the determination of statistical ensembles for two-phase flows
3.14. Statistical analysis of mass exchange in a two-phase flow
3.15. Statistical parameters of mass exchange

4. Checking the adequacy of entropic model of two-phase flows in separation regimes
4.1. Mathematical model of polyfractional mixture redistribution in a multi-stage cascade
4.2. Experimental checking of theoretical conclusions
4.3. Unified separation curves
4.4. Generalizing invariant
4.5. Determining distribution coefficients of solid phase in a two-phase flow 
4.6. Computation of distribution coefficients
4.7. Development of the method of separation processes calculation 
4.8. Determining of generalizing invariants for all separation regimes   
4.9. Relationship between the structural and cellular models of the process
4.10. Generalizing criteria

5. Place of the entropy parameter in modern science
5.1. Problematical character of entropy
5.2. General properties of entropy
5.3. Development as an increasing complexity
а. Physical complexity
b. Biological complexity
с. Development of civilization
5.4. Biological systems and Darwinism
5.5. Basic aspects of entropy
5.6. Some world-view aspects of entropy
5.7. Conclusion


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© Elsevier 2020
22nd July 2020
Paperback ISBN:
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About the Author

Eugene Barsky

The author, Dr. Eugene Barsky, has been engaged in this subject for 18 years, since 1993. His M.Sc. thesis completed in 1998 was devoted to the development of models of cascade separation of solid materials in flows. His PhD thesis completed in 2001 was devoted to the development of entropy criterion of separation processes optimization. Among dozens of criteria applied, the entropy criterion has proved to be the most unbiased one. Since that time, the author has been developing these topics in depth. He created a number of industrial cascade apparatuses for powders separation and dust collection, wrote about 20 articles, published two books, participated in many scientific congresses and conferences. The material accumulated during 6 recent years is presented in the proposed book.

Affiliations and Expertise

Department of Industrial Engineering, Azrieli College of Engineering, Jerusalem, Israel

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