3_2020_sen_10

Title of the article

DEVELOPMENT OF THE CONCEPT OF ENTROPY: FROM THERMODYNAMICS TO COSMOLOGY. PART 1. THE CONCEPT OF ENTROPY: THERMODYNAMICS, MECHANICS, INFORMATICS, TRIBO-FATIGUE, MECHANOTHERMODYNAMICS
Authors

SOSNOVSKIY Leonid A., D. Sc. in Eng., Prof., Professor of the Department “Locomotives”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

SHERBAKOV Sergei S., D. Sc. in Phys. and Math., Prof., Professor of the Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section TRIBO-FATIGUE SYSTEMS MECHANICS
Year 2020 Issue 3 Pages 78–88
Type of article RAR Index UDK 536 Index BBK  
DOI https://doi.org/10.46864/1995-0470-2020-3-52-78-88
Abstract The paper describes a mathematical approach to the concept of entropy. Its analysis is given in various fields of science (thermodynamics, mechanics, etc.) and a summary of the main “entropy laws” is compiled. Seven useful definitions of entropy for additive processes (systems) are formulated. It is emphasized that thermodynamic entropy is not a conserved quantity, cannot be observed directly, and has no material content. These three “not” significantly complicate the use of the concept of entropy in engineering applications. It has been established that the concepts of entropy are fundamentally different for additive and non-additive processes (systems). For the former, entropy (in thermodynamics) is a characteristic of energy dissipation. And for the latter (in tribo-fatigue) this is a characteristic of its absorption. In mechanothermodynamics, both of these processes are analyzed. In this case, between the energy components (and, therefore, entropy, as well as damage to system elements caused by loads of different nature), specific interactions arise. It is shown that Λ-functions at the macro level turn out to be completely analogous to the non-additivity parameters in the q-calculus (at the nanoscale). This indicates the fundamental nature of modern concepts of non-additive systems. The basic concepts of tribo-fatigue and mechanothermodynamic entropy are presented. Their following features are established: an object (a system of interacting media, not a medium); the state of the object (current and limiting, not just current); not dispersed, but effective energy spent directly on the production of damage; non-additivity (the interaction of energy components, entropy, damage caused by loads of different nature). The universal law of steady growth of entropy is written and analyzed. It is shown that the evolution of the system in the general case is determined by the intensity of the processes of irreversible changes in entropy — thermodynamic and tribo-fatigue, i.e. combined mechanothermodynamic entropy. And entropy production is as eternal as movement and damage. That is why the concept of entropy has proved useful in cosmology. In this regard, the well-known analogy of thermodynamics and mechanics of black holes in cosmology is recognized as insufficient. A hypothesis is put forward on the analogy of mechanothermodynamics and mechanics of black holes based on the concepts of tribo-fatigue and mechanothermodynamic entropy. The first substantiation of this analogy is given and its prospects are analyzed. The article is published in two parts.
Keywords

entropy, thermodynamics, reversible and irreversible processes, statistical mechanics, classical dynamics, quantum mechanics, continuum mechanics, friction and wear mechanics, mechanical fatigue, informatics, tribofatigue, mechanothermodynamics, mechanics of black holes, systems evolution
  You can access full text version of the article.
Bibliography
  1. Clausis R. Hirst T.A., Tyndall J. Mechanical Theory of Heat. London, John van Voorst, 1867. 376 p.
  2. Kondepudi D., Prigogine I. Modern Thermodynamics: From Heat Engines to Dissipative Structures. John Wiley & Sons, 1998. 486 p.
  3. Fizicheskiy entsiklopedicheskiy slovar [Physical encyclopedic dictionary]. Moscow, Bolshaya sovetskaya entsiklopediya Publ., 1983. 928 p. (in Russ.).
  4. Wikipedia. The Free Encyclopedia. Available at: https://en.wikipedia.org/wiki/Entropy (accessed 10 May 2020).
  5. Atkins P.W. The Second Law. W.H. Freeman & Co., 1984. 230 p.
  6. Eddington A.S. The Nature of Physical World. Gifford Lectures. Brooklyn, AMS Press, 1927. 382 p.
  7. Boltzmann L. Sitzungsber. Academie der Wissenschaften Wien, 1872, vol. 66, pp. 275–370.
  8. Planck M. Treatise on Thermodynamics. New York, Dover, 1945.
  9. Shannon K. Raboty po teorii informatsii i kibernetike [Works on information theory and cybernetics]. Moscow, Inostrannoy literatury Publ., 1963. 832 p. (in Russ.)
  10. Tribus M., McIrvine E.C. Energy and Information. Scientific America, 1971, vol. 224, pp. 178–189.
  11. Gibbs J.W. The Scientific Papers of Willard Gibbs. Vol. 1. Thermodynamics. New York, Dover, 1961.
  12. Coveney P.V. The Second Law of Thermodynamics: Entropy, Irreversibility and Dynamics. Nature, 1988, vol. 333, pp. 409–415.
  13. Von Neumann J. Mathematische Grundlagen der Quantenmechanik. Springer, 1996. 271 p.
  14. Mase G.E. Theory and Problems of Continuum Mechanics. New York, Mcgraw-Hill Book Company, 1970.
  15. Sedov L.I. Mekhanika sploshnoy sredy. Tom 2 [Mechanics of a continuous medium. Volume 2]. Moscow, Nauka Publ., 1973. 420 p. (in Russ.).
  16. Bryant M.D. Entropy and Dissipative Processes of Friction and Wear. Transactions of Faculty of Mechanical Engineering, 2009, vol. 37, no. 2, pp. 55–60.
  17. Naderi M., Amiri M., Khonsari M.M. On the thermodynamic entropy of fatigue fracture. Proceedings of the Royal Society, Series A, 2010, no. 466, pp. 423–438.
  18. Khinchin A.Ya. Ponyatiye entropii v teorii veroyatnostey [The concept of entropy in probability theory]. Russian Mathematical Surveys, 1953, vol. 8, no. 3(55), pp. 3–20 (in Russ.).
  19. Vysotsky M.S., Vityaz P.A., Sosnovskiy L.A. Mekhanotermodinamicheskaya sistema kak novyy obekt issledovaniya [Mechanothermodynamic system as a new object of research]. Mechanics of machines, mechanisms and materials, 2011, no. 2(15), pp. 5–10 (in Russ.).
  20. Sosnovskiy L.A., Sherbakov S.S. Mechanothermodynamics. Berlin, Springer, 2016. 155 p.
  21. Sherbakov S.S. Modeli sostoyaniy tribofaticheskikh i mekhanotermodinamicheskikh sistem [Models of states of tribo-fatigue and mechanothermodynamic systems]. Aktualnye voprosy mashinovedeniya, 2019, iss. 8, pp. 204–208 (in Russ.).
  22. Sosnovskiy L.A., Sherbakov S.S. Printsipy mekhanotermodinamiki [Principles of mechanothermodynamics]. Gomel, Belorusskiy gosudarstvennyy universitet transporta Publ., 2013. 150 p. (in Russ.).
  23. Sosnovskiy L.A., Sherbakov S.S. Mechanothermodynamical system and its behavior. Continuum Mechanics and Thermodynamics, 2012, vol. 24, iss. 3, pp. 239–256.
  24. Sosnovskiy L.A. Mekhanika iznosoustalostnogo povrezhdeniya [Mechanics of wear-fatigue damage]. Gomel, Belorusskiy gosudarstvennyy universitet transporta Publ., 2007. 434 p. (in Russ.).
  25. Sherbakov S.S., Sosnovskiy L.A. Mekhanika tribofaticheskikh sistem [Mechanics of tribo-fatigue systems]. Minsk, Belorusskiy gosudarstvennyy universitet Publ., 2010. 407 p. (in Russ.).
  26. Sosnovskiy L.A. Osnovy tribofatiki: v 2-kh tomakh [Fundamentals of Tribo-Fatigue: in 2 volumes]. Gomel, Belorusskiy gosudarstvennyy universitet transporta Publ., 2003. 480 p. (in Russ.).
  27. Adib A.B., Moreira A.A., Andrade Jr. J.S., Almeida M.P. Tsallis thermostatistics for finite systems: a Hamiltonian approach. Physica A: Statistical Mechanics and its Applications, 2003, vol 322, pp. 276–284.
  28. Olemskoi A.I., Yushchenko O.V., Badalyan A.Yu. Statisticheskaya teoriya polya neadditivnoy sistemy [Statistical field theory of a non-additive system]. Theoretical and Mathematical Physics, 2013, vol. 174, no. 3, pp. 444–466 (in Russ.).
  29. Sosnovskiy L.A. Ob odnom vide entropii kak mere pogloshcheniya energii, raskhoduemoy na proizvodstvo povrezhdeniy v mekhanotermodinamicheskoy sisteme [On a form of entropy as a measure of the absorption of energy spent on damage production in a mechanothermodynamic system]. Doklady of the National Academy of Sciences of Belarus, 2007, vol. 51, no. 6, pp. 100–104 (in Russ.).
  30. Sosnovskiy L.A., Sherbakov S.S., Lazarevich A.A. Osnovy teorii evolyutsii neorganicheskikh i organicheskikh sistem, v tom chisle zhivykh i razumnykh [Fundamentals of the theory of evolution of inorganic and organic systems, including living and rational]. Natsionalnaya filosofiya v globalnom mire. Materialy Pervogo belorusskogo filosofskogo kongressa [National Philosophy in the Global World. Proc. First Belarusian Philosophical Congress]. Minsk, 2018, pp. 155–178 (in Russ.).
  31. Sosnovskiy L.A. Tribofatika: o dialektike zhizni [Tribo-Fatigue: on the dialectic of life]. Gomel, Belorusskiy gosudarstvennyy universitet transporta Publ., 1999. 116 p. (in Russ.)
  32. Feynman R. Lektsii po fizike. Tom 4 [Lectures in Physics. Volume 4]. Moscow, Mir Publ., 1963. 261 p. (in Russ.).