Extended Einstein relations with a complex effective temperature in a one-dimensional driven lattice gas

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Condensed Matter Theory

Background:

• The Einstein relation connects diffusion (D), susceptibility (chi), and conductivity (sigma) in equilibrium systems.
• Linear response theory relies on the Einstein relation for systems near equilibrium.
• Steady states far from equilibrium often violate equilibrium-based relations.

Purpose of the Study:

• To investigate the validity of the Einstein relation in non-equilibrium steady states.
• To extend the Einstein relation for systems driven far from equilibrium.
• To establish new relations between measurable quantities in driven lattice gases.

Main Methods:

• Numerical experiments on a one-dimensional driven lattice gas.
• Measurement of bulk density diffusion constant (D), conductivity (sigma), and density fluctuation intensity (chi).
• Definition of a complex effective temperature (theta-iphi) from static response to a potential.

Main Results:

• The standard Einstein relation (Dchi=sigmaT) does not hold in non-equilibrium steady states.
• A generalized Einstein relation, Dchi=sigmatheta, using the real part of the effective temperature (Theta), is numerically confirmed.
• A new relation, (L/2pi)cchi=sigmaphi, involving propagation velocity (c) and imaginary part of effective temperature (phi), is discovered.

Conclusions:

• The Einstein relation requires modification for non-equilibrium steady states.
• A complex effective temperature provides a framework for generalizing equilibrium relations.
• The study introduces new quantitative relationships for driven systems far from equilibrium.