A Tiling Approach to Counting Inherent Structures in Hard Potential Systems

S. S. Ashwin; Richard K Bowles

doi:10.1016/j.jnoncrysol.2009.01.038

Home/Archive/arXiv

arXiv · 0903.1874

A Tiling Approach to Counting Inherent Structures in Hard Potential Systems

S. S. Ashwin·Richard K Bowles

View original source ↗Read source document ↗Export metadata ↓

Abstract

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure corresponds to a collectively jammed configuration. This work develops a tiling based approach to counting inherent structures that constructs packings by combining sets of elementary locally jammed structures but eliminates those final packings that either, do not tile space, or are not collectively jammed, through the use of tile incompatibility rules. The resulting theory contains a number of geometric quantities, such as the number of growth sites on a tile and the number of tile compatibilities that provide insight into the number of inherent structures in certain limits. We also show that these geometric quantities become quite simple in a system of highly confined hard discs.

Explore related subjects

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

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

S. S. Ashwin, Richard K Bowles. 2009-03-10. A Tiling Approach to Counting Inherent Structures in Hard Potential Systems. https://doi.org/10.1016/j.jnoncrysol.2009.01.038

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

KEEP EXPLORING

Related papers

arXiv2026

Information geometry of perturbed gradient flow systems on hypergraphs: A perspective towards nonequilibrium physics

This article serves to concisely review the link between gradient flow systems on hypergraphs and information geometry which has been established within the last five years. Gradient flow systems describe a wealth of physical phenomena and provide powerful analytical technquies which are based on the variational energy-dissipation principle. Modern nonequilbrium physics has complemented this classical principle with thermodynamic uncertaintly relations, speed limits, entropy production rate decompositions, and many more. In this article, we formulate these modern principles within the framework of perturbed gradient flow systems on hypergraphs. In particular, we discuss the geometry induced by the Bregman divergence, the physical implications of dual foliations, as well as the corresponding infinitesimal Riemannian geometry for gradient flow systems. Through the geometrical perspective, we are naturally led to new concepts such as moduli spaces for perturbed gradient flow systems and thermodynamical area which is crucial for understanding speed limits. We hope to encourage the readers working in either of the two fields to further expand on and foster the interaction between the two fields.

cond-mat.stat-mech↗

arXiv2026

Kinetic Interference in Translational Control: A Path-Measure Framework for Collision-Triggered Transcript Decay

I connect two literatures developed independently: the path-measure formulation of non-equilibrium statistical mechanics, where a trajectory action decomposes into a time-antisymmetric (entropic) and time-symmetric (frenetic) sector, and the stochastic modelling of ribosomal traffic on messenger RNA. The biological target is a proposed intervention -- antisense oligonucleotide (ASO) interference with wobble-uridine (U34) modification of transfer RNA -- whose intended effect is not to abolish translation but to perturb its timing, driving ribosome collisions and collision-triggered transcript decay preferentially on high-flux, codon-biased transcripts. Dynamical-activity and large-deviation analyses of generic lattice exclusion models -- notably the symmetric and totally asymmetric simple exclusion processes -- are well established. To my knowledge their formalization specifically for ribosomal traffic queues, translation elongation, and collision-triggered no-go decay remains unoccupied; this paper addresses that narrower gap, not the general one. Two claims here are load-bearing and untested. First, selectivity: transcripts whose loss is therapeutically desirable are separable, by vulnerable-codon-pair burden, from transcripts whose loss is toxic. Second, non-redundancy: the frenetic decomposition yields predictions, specific to ribosomal queueing and collision-triggered decay, not already obtainable from rate-level exclusion-process models or existing activity/large-deviation analyses of exclusion processes. This paper establishes neither. It specifies both as falsifiable tests with pre-registered decision rules, including outcomes under which the framework should be abandoned or narrowed. It is a research programme proposal, not a result. No new experimental, computational, or bioinformatic results are reported.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic efficiency of communication channels

We identify a broad class of communication channels that captures common physical constraints in both artificial and natural systems and derive bounds on their thermodynamic cost. We find that the entropy production per channel use is bounded from below by the input-output mutual information, and their ratio -mutual information divided by entropy production- defines the thermodynamic efficiency. Unlike previous studies of energy-constrained communication channels, our analysis shows that thermodynamic costs must be assigned not only to the input symbols themselves, but also to transitions between successive symbols. As a result, maximizing thermodynamic efficiency favors a biased input that switches only rarely, rather than the capacity-achieving input. For the binary symmetric channel, this preference emerges through a pitchfork bifurcation that spontaneously breaks the symmetry of the channel. A minimal model of cellular sensing exhibits the same phenomenon.

cond-mat.stat-mech↗