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.
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