Nonequilibrium Steady States in Driven Lattice Gas Models

Abstract

Systems driven far from equilibrium by an external field or boundary reservoirs settle into nonequilibrium steady
states (NESS) whose statistics of current and entropy production remain difficult to predict from microscopic rules
alone. We study a two-dimensional driven lattice gas on a periodic L x L lattice subject to an external field E that
biases particle hopping along one axis, using kinetic Monte Carlo simulation across 42 combinations of field
strength (E = 0.5 to 8.0, in units of k_BT per lattice spacing) and particle density (rho = 0.2 to 0.6) on lattices ranging
from L = 32 to L = 128. For each combination we ran 2.0 x 10^7 Monte Carlo steps after a 4.0 x 10^6-step
equilibration window and computed the stationary particle current, the steady-state entropy production rate via the
Lebowitz-Spohn functional, and the variance of the time-integrated current using 200 independent trajectories per
condition. Mean particle current increased with field strength but saturated above E = 5.0, reaching 0.312 particles
per site per MC sweep at rho = 0.4, only 6% above its value at E = 4.0, indicating a crossover from field-linear to
saturated transport. Entropy production rate scaled consistently with the product of current and field over the entire
explored range (R^2 = 0.981), confirming the expected linear-response-violating but thermodynamically consistent
relation sigma = E * J even deep in the nonlinear regime. Current variance exhibited pronounced sub-linear growth
with system size at high density (rho = 0.6), with the scaled cumulant ratio falling to 0.71 of its dilute-limit value at L
= 128, consistent with the anomalous, long-range density correlations expected in driven diffusive systems of this
universality class. A finite-size scaling analysis of the current variance gave a scaling exponent of 0.34 +/- 0.03,
distinguishable from the equilibrium diffusive value of 0.50 at the 95% confidence level (bootstrap, 5000 resamples).
These results provide quantitative benchmarks for current fluctuation theorems in a canonical driven lattice model
and support the use of the Lebowitz-Spohn entropy functional as a practical diagnostic for detailed-balance violation
strength in simulated NESS across a broad range of driving conditions.