Abstract
Kinetic theory is reviewed for dilute gases for a microscopic derivation of stochastic models for the Brownian motion. We first derive a pseudo-Liouville equation for an intuitive toy model of collision for illustration. We next derive the pseudo-Liouville equation and the corresponding BBGKY hierarchy for a hard-core system composed of gas and a tracer particle. By assuming molecular chaos, the non-linear and the linear Boltzmann equations are derived for the gas and tracer particles, respectively. Application to modeling fluctuation is finally investigated.
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Notes
- 1.
The collisional force is irrelevant to the rotational degrees of freedom on this condition.
- 2.
In the presence of inelastic collisions (e.g., granular gases), a constant factor appears for modification [3].
- 3.
This replacement is not correct for inelastic collisions, and the inverse collision formula has to be applied.
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Kanazawa, K. (2017). Kinetic Theory for Dilute Gas. In: Statistical Mechanics for Athermal Fluctuation. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6332-9_3
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DOI: https://doi.org/10.1007/978-981-10-6332-9_3
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