Low-temperature anomalies in one-dimensional exactly solvable fluids

TL;DR

This paper investigates the presence of negative thermal expansion in exactly solvable one-dimensional fluids, revealing conditions under which NTE occurs, especially related to soft potentials and their curvature, with implications for thermodynamic behavior.

Contribution

It demonstrates that NTE can occur in classical one-dimensional fluids with specific soft potentials, and clarifies the role of potential curvature and singularities in this phenomenon.

Findings

NTE is absent in quantized pure hard rods.

Certain soft potentials induce NTE at low temperatures.

Compressibility is characterized by plateau features in isotherms.

Abstract

Previous experiments and numerical simulations have revealed that a limited number of two- and three-dimensional particle systems contract in volume upon heating isobarically. This anomalous phenomenon is known as negative thermal expansion (NTE). The present paper focuses on the possibility of NTE in exactly solvable one-dimensional fluids. Firstly, the quantization of classical pure hard rods (free of NTE) does not induce NTE which indicates an unimportant role of quantum mechanics in the topic. Secondly, the classical hard rods with various types of soft nearest-neighbor interactions that contain a basin of attraction with only one minimum are investigated. The ground-state analysis reveals that, for certain potentials, increasing the pressure can lead to a discontinuous jump in the mean spacing between particles. The low-temperature analysis of the exact equation of state indicates that the NTE anomaly is present if the curvature of the soft potential increases with the distance between particles or if the potential exhibits a singularity within the basin of attraction. Isotherms of the compressibility factor, which measures the deviation of the thermodynamic behavior of a real gas from that of an ideal gas, demonstrate typical plateau or double-plateau shapes in large intervals of particle density.