Nonequilibrium phenomena: II. Stochastic Methods
Instead of trying to present a sketch of the theory of Markovian stochastic processes, which is certainly beyond the scope of this text, we discuss some examples of the application of stochastic methods to analyze systems of physical interest. Initially, we introduce the Langevin and the Fokker-Planck equations for the Brownian motion, as investigated by Einstein and Smoluchowski during the early years of the twentieth century. We then present some probabilistic arguments to establish a master equation, which gives the time evolution of the probability of occurrence of the microscopic configurations of a physical system. However, as we have already pointed out, to obtain the transition probabilities of a master equation is usually as difficult as to satisfactorily decouple the BBGKY hierarchical set of kinetic equations.
KeywordsBrownian Motion Master Equation Ising Model Langevin Equation Detailed Balance
Unable to display preview. Download preview PDF.