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Thermostating by Deterministic Scattering: The Periodic Lorentz Gas

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Abstract

We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process. We apply our method to the periodic Lorentz gas, where a point particle moves diffusively through an ensemble of hard disks arranged on a triangular lattice. First, collision rules are defined for this system in thermal equilibrium. They determine the velocity of the moving particle such that the system is deterministic, time-reversible, and microcanonical. These collision rules can systematically be adapted to the case where one associates arbitrarily many degrees of freedom to the disk, which here acts as a boundary. Subsequently, the system is investigated in nonequilibrium situations by applying an external field. We show that in the limit where the disk is endowed by infinitely many degrees of freedom it acts as a thermal reservoir yielding a well-defined nonequilibrium steady state. The characteristic properties of this state, as obtained from computer simulations, are finally compared to those of the so-called Gaussian thermostated driven Lorentz gas.

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Authors and Affiliations

  1. Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, B-1050, Brussels, Belgium

    K. Rateitschak, R. Klages & G. Nicolis

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  1. K. Rateitschak
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  2. R. Klages
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  3. G. Nicolis
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Rateitschak, K., Klages, R. & Nicolis, G. Thermostating by Deterministic Scattering: The Periodic Lorentz Gas. Journal of Statistical Physics 99, 1339–1364 (2000). https://doi.org/10.1023/A:1018645007533

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