# How the overlap of excluded volume determines the configurational energy landscape and "thermodynamics" in the "one to five hard disks in a box" system

## TL;DR

This paper investigates how excluded volume overlaps influence the energy landscape and thermodynamics in small hard disk systems, revealing the importance of second-neighbor interactions in phase behavior.

## Contribution

It analytically and numerically demonstrates that second-neighbor excluded volume interactions significantly affect the energy landscape in hard disk systems.

## Key findings

- Second-neighbor excluded volume interactions are crucial for energy landscape topology.
- Attractive forces arise from excluded volume overlap, affecting system behavior.
- Second-neighbor interactions are linked to phase transitions in hard-core systems.

## Abstract

In this work, the effects of excluded volume are studied in the "one to five hard disks in a box" system. For one and two disks in different types of cages, the attractive and repulsive forces are calculated analytically. Attractive forces are due to excluded volume overlap, and thus allows to understand that in hard-core systems, second neighbors have an effective interaction, a fact that is usually neglected when considering only collisions with first-neighbors. The same effects are observed for numerical computations with five-disks in a box, as the distributions of distances between disks and disks to walls suggest. The results indicate that first and second-neighbor excluded volume interactions are essential to determine the energy landscape topology. This work supports previous observations that suggests that second-neighbor excluded volume interactions in hard-core systems are related with phase transitions.