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.
1. Introduction - p. xiii 2. 1. Brief history: properties and problems of entropy parameter - p. 1 3. 2. Statistical entropy component - p. 39 4. Abstract - p. 39 5. 2.1 Notions of randomness, chaos, and stability - p. 39 6. 2.2 Probabilistic characteristics - p. 40 7. 2.3 Random values and distribution functions - p. 44 8. 2.4 Probabilistic interpretation of granulometric characteristics of the solid phase of a polyfractional mixture of solid particles - p. 45 9. 2.5 Determining average values of random quantities - p. 49 10. 2.6 Importance of unambiguous evaluation of complex compositions of various systems - p. 53 11. 2.7 Uncertainty of mixture compositions - p. 54 12. 2.8 Separation efficiency - p. 61 13. 2.9 Separation optimality condition according to entropic criterion for binary mixtures - p. 62 14. 2.10 Unbiased evaluation of the efficiency of multicomponent mixtures separation - p. 67 15. 2.11 Example of optimization of separation into four components - p. 71 16. 2.12 Mathematical model of separation into n components - p. 78 17. 2.13 Unambiguous evaluation of completeness of a complicated object in the process of construction - p. 84 18. 2.14 Unambiguous evaluation of complex processing of natural resources - p. 91 19. 3. Dynamic component of entropy - p. 95 20. Abstract - p. 95 21. 3.1 Modeling and analogy—the basis of dynamic systems comprehension - p. 95 22. 3.2 Substantiation of the physical analogy - p. 97 23. 3.3 Foundations of the statistical model of critical two-phase flows - p. 102 24. 3.4 Definition of distribution parameters - p. 106 25. 3.5 Substantiation of the entropy parameter for two-phase flows - p. 115 26. 3.6 Main properties of dynamic entropy characterizing a two-phase system - p. 123 27. 3.7 Stationary state as a condition of entropy maximality - p. 128 28. 3.8 On the issue of entropy parameter formation for dynamic systems - p. 135 29. 3.9 Entropy and probabilities distribution - p. 137 30. 3.10 Multidimensional statistical model of a two-phase system - p. 144 31. 3.11 Two-phase flow mobility - p. 150 32. 3.12 Other invariants for two-phase flows - p. 153 33. 3.13 Canonical distributions in the definition of statistical ensembles for two-phase flows - p. 159 34. 3.14 Statistical analysis of mass exchange in a two-phase flow - p. 166 35. 3.15 Statistical parameters of mass transfer - p. 178 36. 4. Verification of the entropic model adequacy for two-phase flows in separation conditions - p. 193 37. Abstract - p. 193 38. 4.1 Mathematical model of poly-fractional mixture redistribution in a multistage cascade - p. 193 39. 4.2 Experimental check of theoretical conclusions - p. 199 40. 4.3 Unifiеd separation curves - p. 208 41. 4.4 Generalizing invariant - p. 215 42. 4.5 Determination of solid-phase distribution coefficients in a two-phase flow - p. 217 43. 4.6 Estimation of distribution coefficients - p. 228 44. 4.7 Development of the methodology of separation processes computation - p. 234 45. 4.8 Definition of generalizing invariants for all separation regimes - p. 239 46. 4.9 Correlation of structural and cellular models of the process - p. 242 47. 4.10 Generalizing criteria - p. 246 48. 5. Place of the entropy parameter in technical sciences and other branches of knowledge - p. 251 49. Bibliography - p. 279 50. Index - p. 283
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.
1. Introduction - p. xiii 2. 1. Brief history: properties and problems of entropy parameter - p. 1 3. 2. Statistical entropy component - p. 39 4. Abstract - p. 39 5. 2.1 Notions of randomness, chaos, and stability - p. 39 6. 2.2 Probabilistic characteristics - p. 40 7. 2.3 Random values and distribution functions - p. 44 8. 2.4 Probabilistic interpretation of granulometric characteristics of the solid phase of a polyfractional mixture of solid particles - p. 45 9. 2.5 Determining average values of random quantities - p. 49 10. 2.6 Importance of unambiguous evaluation of complex compositions of various systems - p. 53 11. 2.7 Uncertainty of mixture compositions - p. 54 12. 2.8 Separation efficiency - p. 61 13. 2.9 Separation optimality condition according to entropic criterion for binary mixtures - p. 62 14. 2.10 Unbiased evaluation of the efficiency of multicomponent mixtures separation - p. 67 15. 2.11 Example of optimization of separation into four components - p. 71 16. 2.12 Mathematical model of separation into n components - p. 78 17. 2.13 Unambiguous evaluation of completeness of a complicated object in the process of construction - p. 84 18. 2.14 Unambiguous evaluation of complex processing of natural resources - p. 91 19. 3. Dynamic component of entropy - p. 95 20. Abstract - p. 95 21. 3.1 Modeling and analogy—the basis of dynamic systems comprehension - p. 95 22. 3.2 Substantiation of the physical analogy - p. 97 23. 3.3 Foundations of the statistical model of critical two-phase flows - p. 102 24. 3.4 Definition of distribution parameters - p. 106 25. 3.5 Substantiation of the entropy parameter for two-phase flows - p. 115 26. 3.6 Main properties of dynamic entropy characterizing a two-phase system - p. 123 27. 3.7 Stationary state as a condition of entropy maximality - p. 128 28. 3.8 On the issue of entropy parameter formation for dynamic systems - p. 135 29. 3.9 Entropy and probabilities distribution - p. 137 30. 3.10 Multidimensional statistical model of a two-phase system - p. 144 31. 3.11 Two-phase flow mobility - p. 150 32. 3.12 Other invariants for two-phase flows - p. 153 33. 3.13 Canonical distributions in the definition of statistical ensembles for two-phase flows - p. 159 34. 3.14 Statistical analysis of mass exchange in a two-phase flow - p. 166 35. 3.15 Statistical parameters of mass transfer - p. 178 36. 4. Verification of the entropic model adequacy for two-phase flows in separation conditions - p. 193 37. Abstract - p. 193 38. 4.1 Mathematical model of poly-fractional mixture redistribution in a multistage cascade - p. 193 39. 4.2 Experimental check of theoretical conclusions - p. 199 40. 4.3 Unifiеd separation curves - p. 208 41. 4.4 Generalizing invariant - p. 215 42. 4.5 Determination of solid-phase distribution coefficients in a two-phase flow - p. 217 43. 4.6 Estimation of distribution coefficients - p. 228 44. 4.7 Development of the methodology of separation processes computation - p. 234 45. 4.8 Definition of generalizing invariants for all separation regimes - p. 239 46. 4.9 Correlation of structural and cellular models of the process - p. 242 47. 4.10 Generalizing criteria - p. 246 48. 5. Place of the entropy parameter in technical sciences and other branches of knowledge - p. 251 49. Bibliography - p. 279 50. Index - p. 283
