Area and perimeter distribution of a surface in two dimensions

TL;DR

This paper analyzes the distribution of surface configurations in two dimensions with fixed length and perimeter, comparing analytical approximations with exact algorithms, relevant for entropy calculations in various physical systems.

Contribution

It introduces an approximate analytical method for surface configuration distribution and validates it against exact lattice algorithms.

Findings

Analytical approximation agrees well with exact results

Method applicable to domain growth, evaporation, membrane, and polymer physics

Provides insights into entropy of macroscopic surface configurations

Abstract

We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares favourably with results from an exact algorithm for the discrete lattice. This work is relevant for finding the entropy associated with macroscopic configurations of such systems as domain growth problems, evaporation--deposition problems, membrane physics, or polymer physics.