This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text.
It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given. It also describes relaxation theory of non-stationary Markov periodic in time systems. The theory of finite and infinite transport in disordered networks, with a discussion of the issue of anomalous diffusion is introduced. Further, it provides the basis for establishing the relationship between quantum aspects of the theory of linear response and the calculation of diffusion coefficients in amorphous systems.
"This is an excellent textbook suitable for graduate students interested in nonequilibrium statistical physics and the like. It covers fundamental and advanced topics in the field, which would prepare the students very well for understanding complex systems ... . I will definitely use this textbook in a new course on a related subject ... . Meanwhile, I will keep it as a reference for my research for it contains many techniques and relevant results." (Sujin Suwanna, Mathematical Reviews, April, 2018)
"This book represents a very comprehensive guideline for random variables and processes especially focused on the practical usage of computational techniques required for solving corresponding problems of modern statistical physics and kinetics. ... Finally, the book is concluded by appendices, which give additional basic information about statistical and quantum mechanics as well as some mathematical methods, which can be useful for a reader's reference." (Eugene Postnikov, zbMATH 1378.82002, 2018)