Fluctuation-theory constraint for extensive entropy in Monte-Carlo simulations

TL;DR

This paper introduces a fluctuation-theory constraint for extensive entropy in Monte-Carlo simulations, improving the understanding of size-dependent entropy and energy fluctuations in the Ising model, with implications for material heterogeneity.

Contribution

It proposes a new constraint based on nanothermodynamics that makes entropy extensive and homogeneous in Monte-Carlo simulations, addressing size dependence issues.

Findings

Enhances energy fluctuations in the Ising model.

Makes entropy homogeneous and additive.

Provides a mechanism for material heterogeneity.

Abstract

The entropy per particle in most Monte-Carlo simulations is size dependent due to correlated energy fluctuations. Guided by nanothermodynamics, we find a constraint for the Ising model that enhances the fluctuations and lowers the free energy, while making the entropy homogeneous, additive, and extensive. Although the average interaction energy becomes size dependent, the resulting distribution of energies provides a mechanism for the heterogeneity found in the dynamics of many materials.