Edwards thermodynamics of the jamming transition for frictionless packings: Ergodicity test and role of angoricity and compactivity

Kun Wang, Chaoming Song, Ping Wang, Hernán A. Makse

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Abstract

This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and "thermalization" at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A→0 + and X→0 -. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a "jamming temperature" T J composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O'Hern, showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other out-of-equilibrium systems like Lennard-Jones glasses and their existence does not preclude the use of statistical mechanics for jammed systems.

Original languageEnglish (US)
Article number011305
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number1
DOIs
StatePublished - Jul 25 2012
Externally publishedYes

Fingerprint

jamming
Jamming
Ergodicity
Packing
Thermodynamics
thermodynamics
Ensemble
Energy Landscape
statistical mechanics
Statistical Mechanics
Inhomogeneity
inhomogeneity
Fluctuations
entropy
Microcanonical Ensemble
network analysis
Maximum Entropy Principle
Scaling Relations
Lennard-Jones
Granular Materials

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

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title = "Edwards thermodynamics of the jamming transition for frictionless packings: Ergodicity test and role of angoricity and compactivity",
abstract = "This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and {"}thermalization{"} at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A→0 + and X→0 -. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a {"}jamming temperature{"} T J composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O'Hern, showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other out-of-equilibrium systems like Lennard-Jones glasses and their existence does not preclude the use of statistical mechanics for jammed systems.",
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N2 - This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and "thermalization" at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A→0 + and X→0 -. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a "jamming temperature" T J composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O'Hern, showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other out-of-equilibrium systems like Lennard-Jones glasses and their existence does not preclude the use of statistical mechanics for jammed systems.

AB - This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and "thermalization" at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A→0 + and X→0 -. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a "jamming temperature" T J composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O'Hern, showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other out-of-equilibrium systems like Lennard-Jones glasses and their existence does not preclude the use of statistical mechanics for jammed systems.

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