Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transportL. C. Lapas, I. V. L. Costa, M. H. Vainstein and F. A. Oliveira
International Center of Condensed Matter Physics and Institute of Physics, University of Brasília, CP 04513 70919-970 Brasília-DF, Brazil
received 17 August 2006; accepted in final form 1 December 2006; published February 2007
published online 30 January 2007
Ballistic transportation introduces new challenges in the thermodynamic properties of a gas of particles. For example, violation of mixing, ergodicity and of the fluctuation-dissipation theorem may occur, since all these processes are connected. In this work, we obtain results for all ranges of diffusion, i.e., both for subdiffusion and superdiffusion, where the bath is such that it gives origin to a colored noise. In this way we obtain the skewness and the non-Gaussian factor for the probability distribution function of the dynamical variable. We put particular emphasis on ballistic diffusion, and we demonstrate that in this case, although the second law of thermodynamics is preserved, the entropy does not reach a maximum and a non-Gaussian behavior occurs. This implies the non-applicability of the central limit theorem.
73.23.Ad - Ballistic transport .
05.70.-a - Thermodynamics .
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion .
© Europhysics Letters Association 2007