  We use extensive computer simulations to probe local thermodynamic
equilibrium (LTE) in a quintessential model fluid, the two-dimensional
hard-disks system. We show that macroscopic LTE is a property much stronger
than previously anticipated, even in the presence of important finite size
effects, revealing a remarkable bulk-boundary decoupling phenomenon in fluids
out of equilibrium. This allows us to measure the fluid's equation of state in
simulations far from equilibrium, with an excellent accuracy comparable to the
best equilibrium simulations. Subtle corrections to LTE are found in the
fluctuations of the total energy which strongly point out to the nonlocality of
the nonequilibrium potential governing the fluid's macroscopic behavior out of
equilibrium.
