Statistical Non Equilibrium

This book includes various aspects of non-equilibrium or irreversible statistical mechanics and their relationships with engineering applications. I hope that this book contributes to expanding the predictability of holistic engineering consisting of thermo-, fluid, and particle dynamics.

The importance of thermodynamics, particularly its Second Principle, to all branches of science in which systems with very large numbers of particles are involved cannot be overstated. This book offers a panoramic view of non-equilibrium thermodynamics. Perhaps the two most attractive aspects of thermodynamic equilibrium are its stability and its independence from the specifics of the particular system involved. Does an equivalent exist for non-equilibrium thermodynamics? Many researchers have tried to describe such stability in the same way that the Second Principle describes the stability of thermodynamic equilibrium - and failed.

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.