We study the non-Arrhenius behavior of surface diffusion near the seco
nd-order phase transition boundary of an adsorbate layer. In contrast
to expectations based on macroscopic thermodynamic effects, we show th
at this behavior can be related to the average microscopic jump rate,
which in turn is determined by the waiting-time distribution W(t) of s
ingle-particle jumps at short times. At long times, W(t) yields a barr
ier that corresponds to the rate-limiting step in diffusion. The micro
scopic information in W(t) should be accessible by scanning tunneling
microscopy measurements.