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We investigate the local equilibrium (LE) distribution of a crystal surfacejump process as it approaches its hydrodynamic (continuum) limit in anonstandard scaling regime introduced by Marzuola and Weare. The atypicalscaling leads to a local equilibrium state whose structure is novel, to thebest of our knowledge. The distinguishing characteristic of the new, "rough" LEstate is that the ensemble average of single lattice site observables do notvary smoothly across lattice sites. We investigate numerically and analyticallyhow the rough LE state affects the convergence mechanism via three key limits,and show that by comparison, more standard, "smooth" LE states satisfy strongerversions of these limits.

The Local Equilibrium State of a Crystal Surface Jump Process in the Rough Scaling Regime