Access-limited equilibration and observable-dependent relaxation in lattice-gas systems.

We investigate equilibration dynamics in a lattice-gas model with spatially restricted coupling to a particle reservoir. Using kinetic Monte Carlo simulations, we isolate the role of reservoir-access geometry by comparing spatially uniform exchange with exchange confined to a limited access region while keeping the thermodynamics and diffusion kinetics fixed. Under uniform access, equilibration is diffusion controlled, and relaxation times increase monotonically with diffusion barrier. In contrast, restricted access introduces an additional kinetic bottleneck without altering the final equilibrium state. The resulting slowdown is nonmonotonic: it is most pronounced at intermediate diffusion barriers, where reservoir access and internal diffusion compete, and weakens when intrinsic diffusion becomes the dominant limitation. Under these conditions, equilibration also becomes observable dependent. Coarse observables such as total coverage can suggest stationarity on a different timescale from internal configurational observables such as the fractional occupation f_{O}(t). Sensitivity tests of the stationarity criterion and finite-size checks confirm that the restricted-access delay is not an artifact of the numerical equilibration definition or lattice size. These results show that reservoir accessibility can act as an independent kinetic control parameter, generating delayed and observable-dependent relaxation even when equilibrium thermodynamics remain unchanged.