Edwards entropy and compactivity in a model of granular matter

Abstract

Formulating a statistical mechanics for granular matter remains a significant challenge, in part, due to the difficulty associated with a complete characterization of the systems under study. We present a fully characterized model of a granular material consisting of $N$ two-dimensional, frictionless, hard discs, confined between hard walls, including a complete enumeration of all possible jammed structures. We show the properties of the jammed packings are independent of the distribution of defects within the system and that all the packings are isostatic. This suggests the assumption of equal probability for states of equal volume, which provides one possible way of constructing the equivalent of a microcanonical ensemble, is likely to be vaild for our model. An application of the second law of thermodynamics involving two subsystems in contact shows that the expected spontaneous equilibration of defects between the two is accompanied by an increase in entropy and that the equilibirum, obtained by entropy maximization, is characterized by the equality of compactivities. Finally, we explore the properties of the equivalent to the canonical ensemble for this system.

Accepted PRE

References in corpus (4)

• Entropy and Temperature of a Static Granular Assembly
• Understanding the Frequency Distribution of Mechanically Stable Disk Packings
• The Complete Jamming Landscape of Confined Hard Discs
• A Tiling Approach to Counting Inherent Structures in Hard Potential Systems

Cited by in corpus (19)

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• Measuring the configurational temperature of a binary disc packing
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• Jammed disks in narrow channel: criticality and ordering tendencies
• Another resolution of the configurational entropy paradox as applied to hard spheres
• Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity
• Exact predictions from Edwards ensemble vs. realistic simulations of tapped narrow two-dimensional granular columns
• Disks in a narrow channel jammed by gravity and centrifuge: profiles of pressure, mass density and entropy density
• Inherent Structure Landscape of Hard Spheres Confined to Narrow Cylindrical Channels
• Devising a protocol-related statistical mechanics framework for granular materials
• Arch-based configurations in the volume ensemble of static granular systems
• Statistical mechanics of two-dimensional foams: Physical foundations of the model
• Jammed disks of two sizes and weights in a channel: Alternating sequences
• Jammed disks of two sizes in a narrow channel
• Interacting jammed granular systems
• Jammed disks of two sizes in a channel: segregation driven by steric forces
• Ordering According to Size of Disks in a Narrow Channel