Abstract
It may seem surprising to start our study with Brownian motion; however, it is a paradigm of dissipative and irreversible behavior of a wide variety of systems. The concepts and methods developed for Brownian motion are the most fundamental cornerstones supporting stochastic processes and nonequilibrium statistical mechanics. These cornerstones are essential to the goal of investigating the time-dependent nonequilibrium properties of complex materials. We shall begin with the Markovian process for random walk. It is followed by a phenomenological description of the Langevin equation that links to diffusion and to stochastic relations. A general fluctuation theory is introduced as an example to show how noise with long-range correlation can be determined. This theory is coupled with the presentation of a molecular theory in the derivation of the Fokker-Plank equation. Finally, the important memory effect in the non-Markovian method for dissipative systems is discussed.
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© 2000 Springer-Verlag New York, Inc.
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Chow, T.S. (2000). Brownian Motion. In: Mesoscopic Physics of Complex Materials. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2108-1_2
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DOI: https://doi.org/10.1007/978-1-4612-2108-1_2
Publisher Name: Springer, New York, NY
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