A parameterised equation of state, glass transition and jamming of the hard sphere system

Hongqin Liu

Home/Archive/arXiv

arXiv · 2602.09218

A parameterised equation of state, glass transition and jamming of the hard sphere system

Hongqin Liu

View original source ↗Read source document ↗Export metadata ↓

Abstract

A Gamma-distribution based potential energy landscape (PEL) theory has recently been proposed for supercooled liquids and glasses. This new PEL theory introduces a singularity term in the equation of state (EoS) suitable for representing the pressure of a glassy or jammed system. Using this framework, a parameterised EoS, Z(eta J), is developed with the random-jammed-packing fraction, eta J, as an input. This EoS is capable of accurately calculating the compressibility (pressure) across the entire metastable and glassy region from eta J=0.62 to 0.66, while seamlessly passing through the stable fluid region. Two special cases (paths) are examined in detail. The first path exhibits a singularity at the random close packing eta J=eta rcp=0.64, traversing the metastable region explored by most simulations. Various thermodynamic properties calculated are compared to simulation data, showing excellent agreements. The second case addresses the first analytical EoS for the ideal glass transition in the hard sphere system. Finally, the transport properties of the hard sphere fluid are modeled using the Arrhenius law and the excess entropy scaling law. It is found that both laws fail (with slope changing) at eta=0.555, where the heat capacity peaks and the contributions of inherent structures and jamming effects begin to emerge.

Explore related subjects

cond-mat.soft cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Hongqin Liu. 2026-02-09. A parameterised equation of state, glass transition and jamming of the hard sphere system. https://arxiv.org/abs/2602.09218

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Scale dependent chirality in twist-bend liquid crystals

The discovery of new classes of lyotropic and thermotropic liquid crystals (e.g., twist-bend, splay, and ferroelectric phases), together with significant advances in experimental techniques for their investigation, has renewed interest in a number of physical phenomena that have been studied in classical liquid crystals (nematics, cholesterics, and smectics) for more than a century. In this paper, we revisit one such ''old--new'' problem, recently highlighted in the preprint by A. Ashkinazi, H. Chhabra, A. El Moumane, M. M. C. Tortora, and J. P. K. Doye, ''Chirality Transfer in Lyotropic Twist-Bend Nematics,'' arXiv:2508.03544v1 (2025), in which various mechanisms of chirality transfer from the molecular scale to the structural scale were discussed. Here we present a simple theoretical analysis of chirality transfer within a Landau theory describing the phase transition between cholesteric and chiral twist-bend liquid crystals. We demonstrate that the handedness of the heliconical structure is opposite to that of the parent cholesteric phase. This relationship originates from the orthogonality between the cholesteric director and the vector order parameter characterizing the phase.

cond-mat.soft↗

arXiv2026

Why life is hot

The process of evolution by natural selection leads to phenotypes of increasing fitness. For cellular chemical reaction networks, this means optimising a variety of fitness functions such as robustness, precision, or sensitivity to external stimuli. We argue that these diverse goals can be achieved by a versatile, generic mechanism: coupling chemical reaction networks to reservoirs that are strongly out of equilibrium. Using theory and numerics we show that this mechanism of optimisation comes at the price of significant heat dissipation. We compute the heat flux caused by kinetic proofreading in {\it Escherichia coli} and show that it constitutes a significant fraction of the total heat flux experimentally measured in this model organism. We then demonstrate that the degree of optimality achievable saturates, and that Nature appears to operate near saturation despite high energetic costs. We argue that `life is hot' largely because of the need for a versatile mechanism to optimise a variety of fitness functions.

cond-mat.soft↗

arXiv2026

Understanding Structural Representation in Foundation Models for Polymers

From the relative scarcity of training data to the lack of standardized benchmarks, the creation of effective foundation models for polymers faces significant and multi-faceted challenges. At the core, many of these issues are tied directly to the structural representation of polymers. Here, we present a chemical language foundation model built on using a SMILES-based polymer graph representation (CPG) that incorporates polymer architectural features and connectivity that are often missing in other line notations. This foundation model exhibited excellent performance on 30 different polymer property benchmark datasets. Critical evaluation of the developed representation against other variations in control experiments reveals this approach to be a robust method of representing polymers in language-based foundation models. These experiments also reveal a strong invariance of structural representations to small perturbations, with many variations of structural representation exceeding or equaling state-of-the-art (SOTA) performance. Surprisingly, SMILES representations which are chemically or semantically invalid also provided near or SOTA performance in several instances--underscoring an unexamined blind spot in the development of chemistry language models. Examination of error sources and attention maps for the evaluated structural representations corroborate the findings of the control experiments, highlighting the ability of the model to interpolate SMILES sequence space in a manner that is loosely congruent to chemical and architectural space for polymers. Overall, this work highlights the surprising robustness of chemistry language models to structural representation perturbations and identifies the conditions under which CPG representation provides meaningful advantages.

cond-mat.soft↗