Thermodynamics and structure of simple liquids in the hyperbolic plane

TL;DR

This paper develops a statistical-mechanical framework to analyze the thermodynamics and structure of simple liquids in hyperbolic geometry, extending classical theories to curved spaces and applying them to Coulombic and short-range interaction systems.

Contribution

It generalizes the virial equation and integral-equation approach for fluids in hyperbolic space, enabling analysis of curvature effects on fluid properties.

Findings

Negative curvature influences fluid structure and thermodynamics.

The formalism applies to Coulombic and short-range potential systems.

Curvature modifies the pair correlation functions and pressure relations.

Abstract

We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk thermodynamic pressure to the pair correlation function and we develop the appropriate setting for extending the integral-equation approach of liquid-state theory in order to describe the fluid structure. We apply the formalism and study the influence of negative space curvature on two types of systems that have been recently considered: Coulombic systems, such as the one- and two-component plasma models, and fluids interacting through short-range pair potentials, such as the hard-disk and the Lennard-Jones models.