Nonequilibrium Steady State: Driven Diffusion
Lattice gas with external field — probability current, entropy production, and violation of detailed balance.
Driven lattice gas (Katz-Lebowitz-Spohn 1984): particles hop on a 2D lattice with biased rates.
External field E breaks detailed balance: J_forward/J_backward = e^(E/T). Steady state has persistent current,
entropy production σ = J·E > 0. Phase transition at ρ=0.5: phase-separated strips perpendicular to drive.