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Barkai E. — Stable Equilibrium Based on Lévy Statistics: A Linear Boltzmann Equation Approach
Barkai E. — Stable Equilibrium Based on Lévy Statistics: A Linear Boltzmann Equation Approach



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Название: Stable Equilibrium Based on Lévy Statistics: A Linear Boltzmann Equation Approach

Автор: Barkai E.

Аннотация:

Journal of Statistical Physics, Vol. 115, Nos. 5/6, June 2004, p. 1537-1565.
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, we consider stochastic collision models. The models are a generalization of the Rayleigh collision model, for a heavy one dimensional particle M interacting with ideal gas particles with a mass m << M. Similar to previous approaches we assume elastic, uncorrelated, and impulsive collisions. We let the bath particle velocity distribution function to be of general form, namely we do not postulate a specific form of power-law equilibrium. We show, under certain conditions, that the velocity distribution function of the heavy particle is Levy stable, the Maxwellian distribution being a special case. We demonstrate our results with numerical examples. The relation of the power law equilibrium obtained here to thermodynamics is discussed. In particular we compare between two models: a thermodynamic and an energy scaling approaches. These models yield insight into questions like the meaning of temperature for power law equilibrium, and into the issue of the universality of the equilibrium (i.e., is the width of the generalized Maxwellian distribution functions obtained here, independent of coupling constant to the bath).


Язык: en

Рубрика: Физика/

Тип: Статья

Статус предметного указателя: Неизвестно

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Год издания: 2004

Количество страниц: 29

Добавлена в каталог: 06.10.2013

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