Abstract
This chapter is entirely devoted to a granular gas model. A Langevin equation for a massive tracer is obtained from the linear Boltzmann equation via a Kramers-Moyal expansion in a diluite limit. Such an expansion is not sufficient to observe non equilibrium effects and an equilibrium-like effective regime is obtained, without the presence of memory. In a denser regime, when the molecular chaos fails, the equation for a tracer is well represented by a Langevin equation with memory, and a local velocity field plays the role of an auxiliary variable coupled to the tracer. Finally, a strong assessment of the validity of the “local field” interpretation is given by the numerical verification of the fluctuation relation.
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Villamaina, D. (2014). The Motion of a Tracer in a Granular Gas. In: Transport Properties in Non-Equilibrium and Anomalous Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01772-3_4
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DOI: https://doi.org/10.1007/978-3-319-01772-3_4
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