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Monograph, Moscow, 2024
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Authors: Kolesnichenko A.V.
Non-additive thermodynamics. Elements of theory and applications
The monograph outlines the basic elements of non-additive statistical thermodynamics, designed to describe complex (anomalous) systems, the actual properties of which are outside the scope of classical Boltzmann-Gibbs statistics, in particular, due to the presence within the system of long-range force interaction, memory effects and large correlations of individual parts, as well as the fractal nature of phase space. This violates the most important thermodynamic property - additivity of entropy, which for equilibrium states in the classical case is a consequence of local interaction between the elements of the system. Such anomalous systems reveal not exponential but asymptotically steppe statistical distributions. On the basis of the Jains principle of maximum parametric entropies of Tsallis, Renyi, Sharma-Mittal, Sharma-Taneji-Mittal and Kaniadakis, the book develops a synergetic scheme representing the process of spontaneous (or forced) transition between the states of a complex dynamical system. The author's new results obtained in the framework of non-extensive thermodynamics, related, in particular, to the modeling of various physical and astrophysical systems and self-gravitating objects, are presented. The book, combining rigor and at the same time accessibility of presentation, is of interest to researchers, graduate students and students interested in specific and general natural regularities and methods of their study and comprehension.
fundamentals of non-additive thermodynamics of anomalous systems, generalized equilibrium thermodynamic relations, modeling of various physical and astrophysical systems and self-gravitating objects
Publication language: russian,  pages: 528
Research direction:
Mathematical modelling in actual problems of science and technics
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About authors:
  • Kolesnichenko Aleksandr Vladimirovich, RAS