Statistical Mechanics of liquids and fluids in curved space

TL;DR

This paper reviews recent advances in understanding the statistical mechanics of liquids and fluids in curved spaces, focusing on how curvature affects their phase behavior, thermodynamics, and structure, especially in two-dimensional manifolds.

Contribution

It provides a comprehensive review of the effects of curvature on liquids and fluids, highlighting recent progress and identifying gaps in the understanding of curved space thermodynamics.

Findings

Curvature influences phase transitions in liquids.

Thermodynamic properties are altered by the geometry of the embedding space.

Structural organization of fluids is affected by the curvature of the substrate.

Abstract

In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter on the phase behavior, thermodynamics and structure of simple liquids. Reference will also be made to existing work on three-dimensional curved space and two-dimensional manifolds with varying curvature.