An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics

Abstract

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.