Calculating entropy by Ma’s method for a system of k-mers on a square lattice

Abstract

Random walk of rectangular particles on a square lattice leads to a pattern formation when the hard-core interaction between the particles is assumed. To estimate changes in the entropy during this random walk, we propose a modification of Ma’s method. The 2D sliding window technique was used to divide a system under consideration into subsystems. We used Ma’s “coincidence” method to estimate the total number of possible states for such subsystems. In this study, the accuracy of Ma’s method is studied in a simple combinatory model, both experimentally and theoretically. We determine which definition of “coincidence” for this scheme leads to greater accuracy. Ma’s estimate of the number of possible states for a system of k-mers correlates well with the estimate obtained using a “naive” method.