  In lattice models local pressure on a surface is derived from the change in
the free energy of the system due to the exclusion of a certain boundary site,
while the total force on the surface can be obtained by a similar exclusion of
all surface sites. In these definitions, while the total force on the surface
of a lattice system matches the force measured in a continuous system, the
local pressure does not. Moreover, in a lattice system, the sum of the local
pressures is not equal to the total force as is required in a continuous
system. The difference is caused by correlation between occupations of surface
sites as well as finite displacement of surface elements used in the definition
of the pressures and the force. This problem is particularly acute in the
studies of entropic pressure of polymers represented by random or self-avoiding
walks on a lattice. We propose a modified expression for the local pressure
which satisfies the proper relation between the pressure and the total force,
and show that for ideal polymers in the presence of scale-invariant boundaries
it produces quantitatively correct values for continuous systems. The required
correction to the pressure is non-local, i.e., it depends on long range
correlations between contact points of the polymer and the surface.
