The purpose of this textbook is to bring together, in a self-contained introductory form, the scattered material in the field of stochastic processes and statistical physics. It offers the opportunity of being acquainted with stochastic, kinetic and nonequilibrium processes. Although the research techniques in these areas have become standard procedures, they are not usually taught in the normal courses on statistical physics. For students of physics in their last year and graduate students who wish to gain an invaluable introduction on the above subjects, this book is a necessary tool.
Part 1 Stochastic processes and the master equation: stochastic processes; Markovian processes; master equations; Kramers Moyal expansion; Brownian motion, Langevian and Fokker-Planck equations. Part 2 Distribution, BBGKY hierarchy, density operator: probability density as a fluid; BBGKY hierarchy; microscopic balance equations; density operator. Part 3 Linear nonequilibrium thermodynamics and onsager relations: onsager regretion to equilibrium hipotesis; onsager relations; minimum production of entropy. Part 4 Linear response theory, fluctuation-disipation theorem: correlation functions - definitions and properties; linear response theory; fluctuation-disipation theorem. Part 5 Instabilities and far from equilibrium phase-transitions: instabilities, bifurcations, limit circles; noise induced transitions; pattern formation - reaction-diffusion; pattern propagation.