Processos estocásticos em física: teoria e fundamentos
AUTOR(ES)
Fábio Macêdo Mendes
DATA DE PUBLICAÇÃO
2009
RESUMO
This work discusses some problems in physics using the language of stochastic processes. Firstly, we discuss the relationships between the formalisms of master equations, path integrals, and jumping processes. Each of them is a different prescription to define a Markovian process. Using these formalisms, we discuss the applicability of the classic Langevin model to molecular systems. We show that this model is inadequate to describe the interaction of a Brownian particle with a gas of hard spheres. The discrepancy with respect to the exact solution is ameliorated if the mass of the Brownian particle is much bigger than the mass of the particles in the gas. The generalized Langevin equation that describes non-Markovian systems is also discussed. Again, we raise a criticism to its relevance in the description of molecular systems. In special, we show a simple physical system that violates the fluctuation dissipation theorem. Finally, the we present a method of inferring tendencies from time series data. Differently from other common methods, e.g., moving averages, we obtain both the expected value for the tendency and the associated error. The calculation is done using path integrals and avoids some expensive computations commonly associated to other similar methods such as Gaussian process regression. This procedure is feasible if the sampling rate is high enough in order to be possible to approximate the time series data by a continuous function
ASSUNTO(S)
física estatística fora do equilíbrio séries temporais fisica processos estocásticos
