# Entropies of the Classical Dimer Model

## TL;DR

This paper uses the classical dimer model to study how molecular geometry affects entropy and free energy in biological attachment processes.

## Contribution

A simplified derivation of the dimer model's partition function and new insights into entropy effects from dimer geometry.

## Key findings

- Dimer geometry leads to a persistently nonzero entropy in DNA double helix adsorption.
- Significant charge inversion occurs as binding forces increase relative to thermal energy.
- Simple lattice gas models fail to capture these geometric entropy effects.

## Abstract

Biological processes often involve the attachment and detachment of extended molecules to substrates. Here, the classical dimer model is used to investigate these geometric effects on the free energy, which governs both the equilibrium state and the reaction dynamics. We present a simplified version of Fisher’s derivation of the partition function of a two-dimensional dimer model at filling factor ν=1, which takes into account the blocking of two adjacent sites by each dimer. Physical consequences of the dimer geometry on the entropy that are not reflected in simpler theories are identified. Specifically, for dimers adsorbing on the DNA double helix, the dimer geometry gives a persistently nonzero entropy and there is a significant charge inversion as the force binding the particles to the lattice increases relative to the thermal energy, which is not true of the simple lattice gas model for the dimers, in which all the sites are independent.