2004/04/30 by Kumiko Hayashi, Shin-ichi Sasa · 1 citation
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.71.046143
published as Phys. Rev. E 71, 046143 (2005) · 8 pages, 10 figures
arxiv created 2005/02/04 · openalex publication_date 2005/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We carry out numerical experiments on a one-dimensional driven lattice gas to elucidate the statistical properties of steady states far from equilibrium. By measuring the bulk density diffusion constant D, the conductivity sigma, and the intensity of density fluctuations, chi, we confirm that the Einstein relation Dchi=sigmaT, which is valid in the linear response regime about equilibrium, does not hold in such steady states. Here, T is the environment temperature and the Boltzmann constant is set to unity. Recalling that the Einstein relation provided the first step in the construction of linear response theory, we attempt to extend it to a generalized form valid in steady states far from equilibrium. In order to obtain new relations among measurable quantities, we define a complex effective temperature theta-iphi from studying the static response of the system to a slowly varying potential in space. Replacing T in the Einstein relation by the real part of the effective temperature Theta , we numerically confirm that the relation Dchi=sigmatheta holds in the nonequilibrium steady states far from equilibrium that we study. In addition to this extended form, we find the relation (L/2pi)cchi=sigmaphi , where c represents the propagation velocity of density fluctuations.