Equilibration, Generalized Equipartition, and Diffusion in Dynamical Lorentz Gases

Author

Stephan De Bievre
Paul Ernest Parris, Missouri University of Science and TechnologyFollow

Abstract

We demonstrate approach to thermal equilibrium in the fully Hamiltonian evolution of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a d-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We analytically predict, and numerically confirm, that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature T, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of their free dynamics-they need not be in a state of thermal equilibrium. The temperature T to which the particles equilibrate obeys a generalized equipartition relation, in which the associated thermal energy k_BT is equal to an appropriately defined average of the scatterers' kinetic energy. In the equilibrated state, particle motion is diffusive.

Recommended Citation

S. De Bievre and P. E. Parris, "Equilibration, Generalized Equipartition, and Diffusion in Dynamical Lorentz Gases," Journal of Statistical Physics, vol. 142, no. 2, pp. 356 - 385, Springer New York, Jan 2011.

The definitive version is available at https://doi.org/10.1007/s10955-010-0109-3

Department(s)

Physics

Keywords and Phrases

Diffusion; Equipartition; Thermal equilibrium

International Standard Serial Number (ISSN)

0022-4715

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2011 Springer New York, All rights reserved.

Publication Date

01 Jan 2011