Transport Properties of a Modified Lorentz Gas

Larralde, H., Leyvraz, F. and Mejia-Monasterio, Carlos ORCID: (2003). Transport Properties of a Modified Lorentz Gas. "Journal of Statistical Physics", v. 113 (n. 1/2); pp. 197-231. ISSN 00224715.


Title: Transport Properties of a Modified Lorentz Gas
Item Type: Article
Título de Revista/Publicación: Journal of Statistical Physics
Date: October 2003
ISSN: 00224715
Volume: 113
Faculty: E.T.S. de Ingeniería Agronómica, Alimentaria y de Biosistemas (UPM)
Department: Ingeniería Agroforestal
Creative Commons Licenses: None

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We present a detailed study of the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a Lorentz gas with fixed freely-rotating circular scatterers interacting with point particles via perfectly rough collisions. Upon imposing a temperature and/or a chemical potential gradient, a stationary state is attained for which local thermal equilib- rium holds for low values of the imposed gradients. Transport in this system is normal, in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are non-trivially coupled, satisfying Onsager’s reciprocity relations to within numerical accuracy as well as the Green–Kubo relations. We further show numerically that an applied electric field causes the same currents as the corresponding chemical potential gradient in first order of the applied field. Puzzling discrepancies in higher order effects (Joule heating) are also observed. Finally, the role of entropy production in this purely Hamiltonian system is shortly discussed.

More information

Item ID: 53284
DC Identifier:
OAI Identifier:
DOI: 10.1023/A:1025726905782
Official URL:
Deposited by: Dr. Carlos Mejia-Monasterio
Deposited on: 18 Dec 2018 11:18
Last Modified: 18 Dec 2018 11:18
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