When using lattice models for polymers (e.g. random walks or self avoiding walks) the local entropic pressure is usually defined as the change in the free energy of the system resulting from the exclusion of a lattice site, divided by the appropriate volume element [1]. Similarly, the total force acting on a boundary wall is associated with the exclusion of all lattice sites adjacent to the wall [2]. In real (continuous) systems the integral of a pressure along a wall equals the total force applied to it. This self-evident relation is not satisfied by the pressure and the force defined on a lattice. Such inconsistency is caused by the inability to make infinitesimal perturbations of the position of the boundary on lattice, as well as by the long range correlations between the contact points of the polymer and the boundary.

By taking into account contact point correlations, we define a new (modified) expression for the local entropic pressure in a lattice model for polymers [3]. Our expression is guaranteed to result in the correct total force acting on the boundary of the system upon integration of the pressure. We also show that the modified pressure agrees quantitatively with known results for the pressure of long continuous ideal polymers on scale invariant boundaries in two dimensions [4].

[1] I. Jensen, W. G. Dantas, C. M. Marques, and J. F. Stilck, J. Phys. A Math. Theor. 46, 115004 (2013).

[2] R. Dickman, J. Chem. Phys. 87, 2246 (1987).

[3] Y. Hammer and Y. Kantor, arXiv:1410.1365 (2014).

[4] Y. Hammer and Y. Kantor, Phys. Rev. E 89, 022601 (2014).