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Stochastic Processes and Basic Theorems of Statistical Mechanics

By root - Posted on 09 junho 2011

Fernando Oliveira, Universidade de Brasília
Terça-feira, 10 Maio, 2011 - 16:00

In the last few years a number of fundamental concepts in statistical mechanics have been discussed [1-4]. An ongoing effort has been developed in order to understand basic concepts such as ergodicity [1,2], Khinchin theorem [1], and it has been found that Fluctuation-Dissipation Theorems may fail in some systems [3]. As well, the study of stochastic processes has found a fertile soil in statistical mechanics for reformulation and development of many methods. For example, a basic law such as the second law of thermodynamics can be formulated in a very simple way, and the generalized Langevin's equation provides us with a simple description of the statistics of a dynamical variable subject to a stochastic evolution. In this talk it is shown how a stochastic version of many basic theorems can be readily obtained [5]. Further work in this direction is needed and will open new perspectives.

[1] M. Howard Lee, PRL 98, 190601, 2007.
[2] L. Lapas, R. Morgado, M. Vainstein, J. Rubi, F. Oliveira, PRL 101, 230602, 2007.
[3] I. Costa, R. Morgado, M. Lima, F. Oliveira, EPL 63, 173, 2003.
[4] L. Lapas, I. Costa, M. Vainstein, F. Oliveira, EPL 77, 37004, 2007.
[5] L. Lapas et al., to be published.