Nonequilibrium phenomena: II. Stochastic Methods

  • Silvio R. A. Salinas
Part of the Graduate Texts in Contemporary Physics book series (GTCP)

Abstract

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.

Keywords

Brownian Motion Master Equation Ising Model Langevin Equation Detailed Balance 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Silvio R. A. Salinas
    • 1
  1. 1.Instituto de FisicaUniversidade de São PaoloSão PaoloBrazil

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