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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.

Year 2020 Issue 3 Pages 78–88
Type of article RAR Index UDK 536 Index BBK  
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.

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

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