Tracking Coupled Granular Temperature and Entropy Dynamics in Granular Materials via Dielectric Spectroscopy

arxiv: 2605.19560 · v1 · pith:5ZRHUQ7Wnew · submitted 2026-05-19 · ❄️ cond-mat.soft · cond-mat.stat-mech

Tracking Coupled Granular Temperature and Entropy Dynamics in Granular Materials via Dielectric Spectroscopy

Sophia G. Krastana , Anthony N. Papathanassiou This is my paper

Pith reviewed 2026-05-20 02:55 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech

keywords granular materialsdielectric spectroscopyAdam-Gibbs relationgranular temperatureconfigurational entropyimpedance spectroscopypacking fractionathermal systems

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The pith

The logarithm of dielectric relaxation time scales with granular temperature and entropy according to a modified Adam-Gibbs relation in graphite powder.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that the log of the dielectric relaxation time extracted from complex impedance measurements scales linearly with granular temperature divided by configurational entropy as graphite powder is compacted. Granular temperature and entropy are estimated from changes in packing fraction alone. A sympathetic reader would care because this links athermal granular relaxation to the entropy-controlled dynamics seen in molecular glasses and suggests dielectric methods can monitor internal state changes without destroying the sample. The scaling holds for both loose and dense packing states.

Core claim

By progressively reducing the volume of graphite powder to change its packing fraction, the authors estimate relative configurational entropy and granular temperature from volumetric data while measuring electrical conductivity and capacity via impedance spectroscopy. The logarithm of the dielectric relaxation time derived from the complex impedance scales with granular temperature and entropy across loose and compact states, following the modified Adam-Gibbs relationship.

What carries the argument

Modified Adam-Gibbs law for athermal granular systems relating the logarithm of dielectric relaxation time to granular temperature and configurational entropy estimated from volumetric packing data.

If this is right

Dielectric spectroscopy acts as a non-destructive probe of configurational dynamics in granular matter analogous to its use in polymers and glass formers.
Changes in complex impedance from packing fraction variations are controlled by granule configuration under the AG-like scaling.
The observed scaling relationship applies to both loose and compact granular states.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could enable real-time, non-invasive monitoring of configurational changes during granular compaction or flow in practical applications.
Similar impedance measurements on other particulate systems such as sands or beads could test whether the entropy-temperature scaling generalizes beyond graphite.
The results lend experimental support to the use of Edwards-style statistical mechanics for describing relaxation in athermal granular materials.

Load-bearing premise

Granular temperature and configurational entropy can be appropriately defined and estimated from volumetric data alone in a manner that makes the modified Adam-Gibbs law applicable to this athermal system.

What would settle it

Measuring dielectric relaxation times at multiple packing fractions and finding that the logarithm does not scale linearly with the volumetric estimates of granular temperature over entropy would disprove the central claim.

read the original abstract

In glass-forming liquids, structural dynamics are governed by configurational entropy and temperature, with dielectric relaxation time scaling alongside structural relaxation time as described by the Adam-Gibbs (AG) model. Under Edwards's athermal statistical thermodynamics, a modified AG law similarly governs granular matter, provided that granular temperature and configurational entropy are appropriately defined. This study investigates whether variations in the structural relaxation of granular systems can be probed via thermally activated processes, specifically electric charge hopping and trapping. By progressively reducing the volume of graphite powder to vary its packing fraction, we estimated relative configurational entropy and granular temperature from volumetric data, while evaluating electrical conductivity and capacity via impedance spectroscopy. We demonstrate that the logarithm of the dielectric relaxation time, derived from complex impedance, scales with granular temperature and entropy across both loose and compact states. Consequently, changes in the complex impedance resulting from packing fraction variations are tuned by granule configuration, strictly adhering to an AG-like relationship for thermal systems. These findings establish dielectric spectroscopy as a viable, non-destructive tool for tracing configurational dynamics in granular matter, analogous to its established use in polymers and glass formers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

They apply dielectric spectroscopy to compacted graphite and claim AG-like scaling of relaxation time with volume-derived granular T and S, but the mapping from packing fraction looks under-specified and potentially circular.

read the letter

The main thing to know is that this paper uses impedance spectroscopy on granular graphite while reducing its volume, extracts a dielectric relaxation time from the complex impedance, and reports that log(tau) scales with their estimates of granular temperature and configurational entropy in a modified Adam-Gibbs form across loose and dense states. They position the electrical response as a proxy for configurational dynamics in an athermal system. That combination of method and claim is the new piece relative to prior dielectric work on polymers or glass formers. The experimental setup itself is straightforward and non-destructive, which could matter for practical monitoring of granular materials. They also test both compaction regimes, which is a reasonable way to span configurations. The citations track the relevant Edwards ensemble and AG literature without obvious omissions. The soft spot sits right where the stress-test note flags it: granular temperature and entropy are obtained solely from changes in packing fraction, with no explicit functional forms, no error propagation shown, and no cross-check against particle-scale velocity fluctuations or other independent measures. In the Edwards framework that means the entropy estimate already embeds assumptions about the density of stable states and the conjugate variable to volume. If those assumptions are off, the reported linearity could be an artifact of shared dependence on density rather than evidence for the underlying relation. Without the derivations or validation steps in the full text, it is difficult to judge whether the scaling is demonstrated or assumed. This is the sort of work that would interest people working on athermal thermodynamics or alternative probes for jammed systems. A reader already thinking about dielectric methods in soft matter could pick up the experimental angle even if they end up questioning the entropy mapping. I would send it to peer review rather than desk reject, because the probe idea is concrete and the claim is falsifiable once the volume-to-entropy step is written out clearly. Revisions would need to address that gap directly.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that dielectric spectroscopy on graphite powder, with packing fraction varied by progressive volume reduction, allows extraction of dielectric relaxation time from complex impedance; this time's logarithm scales linearly with the product of granular temperature and configurational entropy (both estimated from volumetric data alone) in a modified Adam-Gibbs form, holding for both loose and compact states and establishing the method as a non-destructive probe of configurational dynamics in athermal granular matter.

Significance. If the volumetric mapping to T_gran and S_conf can be placed on a non-circular, independently validated footing, the result would supply a concrete experimental route to test Edwards-style statistical mechanics in granular systems and extend the AG framework beyond thermal glass formers, with potential utility for non-invasive monitoring of jamming and relaxation.

major comments (3)

[Methods section on entropy/temperature estimation] The manuscript states that relative configurational entropy and granular temperature are estimated from volumetric data (packing-fraction changes), yet supplies neither the explicit functional forms (e.g., the assumed density of states that converts volume reduction into S_conf ~ ln Ω(V)) nor the conjugate definition of T_gran. Because both quantities and the measured relaxation time ultimately trace back to the same packing-fraction variable, the reported linear scaling of log τ with 1/(T_gran S_conf) risks being tautological rather than a test of the modified AG relation.
[Results and Discussion] No cross-check is presented against an independent granular-temperature observable (particle-velocity fluctuations or kinetic-energy spectra). Without such validation, the applicability of the athermal AG construction remains an assumption rather than a demonstrated result.
[Impedance analysis and scaling plots] The extraction of the dielectric relaxation time from the complex-impedance spectra is described only at the level of 'derived from complex impedance'; the fitting model, frequency window, and uncertainty quantification are not given. Consequently the quantitative claim of 'strict adherence' to the AG-like scaling cannot be assessed.

minor comments (2)

[Abstract] Clarify the phrasing in the abstract that the relationship 'strictly adheres to an AG-like relationship for thermal systems'; the system is athermal, so the intended analogy should be stated unambiguously.
[Figures] Any scaling figure should display individual data points with error bars together with the fitted line and a quantitative goodness-of-fit metric so that the strength of the reported linearity can be judged directly.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the presentation of our results on dielectric spectroscopy as a probe of configurational dynamics in granular graphite. We address each major comment below and indicate revisions to be incorporated in the next version of the manuscript.

read point-by-point responses

Referee: [Methods section on entropy/temperature estimation] The manuscript states that relative configurational entropy and granular temperature are estimated from volumetric data (packing-fraction changes), yet supplies neither the explicit functional forms (e.g., the assumed density of states that converts volume reduction into S_conf ~ ln Ω(V)) nor the conjugate definition of T_gran. Because both quantities and the measured relaxation time ultimately trace back to the same packing-fraction variable, the reported linear scaling of log τ with 1/(T_gran S_conf) risks being tautological rather than a test of the modified AG relation.

Authors: We agree that the explicit functional forms and definitions should be stated clearly. In the revised manuscript we will add a dedicated subsection in Methods that specifies the density of states used to obtain S_conf from volume reduction (following the standard Edwards ensemble counting for granular configurations) and the conjugate definition of T_gran. On the question of tautology, the Adam-Gibbs relation imposes a specific functional form—log τ proportional to 1/(T_gran S_conf)—rather than an arbitrary dependence on packing fraction. The observed linearity therefore constitutes a non-trivial test of whether the measured dielectric relaxation obeys this particular relation when T_gran and S_conf are computed from the same volumetric control parameter. We will emphasize this distinction in the revised text. revision: yes
Referee: [Results and Discussion] No cross-check is presented against an independent granular-temperature observable (particle-velocity fluctuations or kinetic-energy spectra). Without such validation, the applicability of the athermal AG construction remains an assumption rather than a demonstrated result.

Authors: We acknowledge that an independent experimental cross-check would strengthen the interpretation. The present work relies on the volumetric definition of granular temperature and configurational entropy that is standard in the Edwards statistical mechanics literature for athermal systems. In the revised manuscript we will expand the Discussion to cite prior experimental and simulation studies that have validated volumetric estimates against velocity-fluctuation measures in similar granular systems, and we will explicitly note the assumptions underlying our choice. A direct particle-tracking comparison lies beyond the scope of this dielectric-spectroscopy study but could be pursued in follow-up work. revision: partial
Referee: [Impedance analysis and scaling plots] The extraction of the dielectric relaxation time from the complex-impedance spectra is described only at the level of 'derived from complex impedance'; the fitting model, frequency window, and uncertainty quantification are not given. Consequently the quantitative claim of 'strict adherence' to the AG-like scaling cannot be assessed.

Authors: We agree that the impedance-analysis procedure requires more detail for reproducibility. In the revised manuscript we will expand the Methods section to specify the equivalent-circuit model employed, the frequency range used for fitting, the criterion for identifying the relaxation time, and the procedure for estimating uncertainties (including propagation from the impedance spectra). Updated scaling plots will include error bars derived from these uncertainties. revision: yes

Circularity Check

0 steps flagged

No significant circularity; estimates of T_gran and S_conf are independent of dielectric data

full rationale

The paper derives relative configurational entropy and granular temperature exclusively from volumetric packing-fraction changes and obtains the dielectric relaxation time separately from complex-impedance spectra. The reported AG-like scaling is therefore an empirical comparison between two independently measured or estimated quantities rather than a quantity that reduces to its own inputs by definition or by fitting. No equations or self-citations in the supplied text indicate that the functional forms of T_gran(φ) or S_conf(φ) were adjusted to the impedance data, nor is any load-bearing premise justified solely by prior work of the same authors. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on the applicability of a modified Adam-Gibbs relation to athermal granular matter once temperature and entropy are suitably defined from volume; no independent evidence for those definitions is supplied in the abstract.

axioms (1)

domain assumption A modified Adam-Gibbs law governs granular matter when granular temperature and configurational entropy are appropriately defined.
Invoked in the abstract as the governing relation for structural dynamics in granular systems.

pith-pipeline@v0.9.0 · 5735 in / 1056 out tokens · 30736 ms · 2026-05-20T02:55:02.853962+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages

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work page doi:10.1021/jp809768y 2009
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work page doi:10.1103/revmodphys.90.015006 2018
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Asenjo, D., Paillusson, F., Frenkel, D.: Numerical calculation of granular entropy. Phys. Rev. Lett. 112, 098002 (2014). https://doi.org/10.1103/PhysRevLett.112.098002

work page doi:10.1103/physrevlett.112.098002 2014
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work page doi:10.1209/0295-5075/114/14004 2016
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Ai, X., Yuan, H., Zhang, S., Zeng, Z., Li, H., Xia, C., Wang, Y .: Testing Adam–Gibbs relationship in tapped granular packings. Commun. Phys. 8, 157 (2025). https://doi.org/10.1038/s42005-025-02070- 9

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Macromolecules 55, 7614–7625 (2022)

Shafqat, N., Alegría, A., Arbe, A., Malicki, N., Dronet, S., Porcar, L., Colmenero, J.: Disentangling the calorimetric glass -transition trace in polymer/oligomer mixtures from the modeling of dielectric relaxation and the input of small -angle neutron scattering . Macromolecules 55, 7614–7625 (2022). https://doi.org/10.1021/acs.macromol.2c0060

work page doi:10.1021/acs.macromol.2c0060 2022
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work page doi:10.1088/1674-1056/26/1/014503 2017
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work page doi:10.1038/ncomms9409 2015
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Physica A 296, 451–459 (2001)

Coniglio, A., Nicodemi, M.: A statistical mechanics approach to inherent states of granular media. Physica A 296, 451–459 (2001). https://doi.org/10.1016/S0378-4371(01)00190-X

work page doi:10.1016/s0378-4371(01)00190-x 2001
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Aste, T., Di Matteo, T.: Emergence of Gamma distributions in granular materials. Phys. Rev. E 77, 021309 (2008). https://doi.org/10.1103/PhysRevE.77.021309

work page doi:10.1103/physreve.77.021309 2008
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work page doi:10.1103/physrevlett.31.44 1973

[1] [1]

: Physics of the granular state

Jaeger, H.M., Nagel, S.R. : Physics of the granular state . Science 255, 1523 –1531 (1992). https://doi.org/10.1126/science.255.5051.1523

work page doi:10.1126/science.255.5051.1523 1992

[2] [2]

de Gennes, P .G.: Granular matter: a tentative view . Rev. Mod. Phys. 71, S374 –S382 (1999). https://doi.org/10.1103/RevModPhys.71.S374

work page doi:10.1103/revmodphys.71.s374 1999

[3] [3]

: The statistical physics of athermal materials

Bi, D., Henkes, S., Daniels, K.E., Chakraborty, B. : The statistical physics of athermal materials . Annu. Rev. Condens . Matter Phys. 6, 63 –83 (2015). https://doi.org/10.1146/annurev-conmatphys- 031214-014336

work page doi:10.1146/annurev-conmatphys- 2015

[4] [4]

Nature 410, 259–267 (2001)

Debenedetti, P.G., Stillinger, F.H.: Supercooled liquids and the glass transition. Nature 410, 259–267 (2001). https://doi.org/10.1038/35065704

work page doi:10.1038/35065704 2001

[5] [5]

: Supercooled liquids and glasses

Ediger, M.D., Angell, C.A., Nagel, S.R. : Supercooled liquids and glasses . J. Phys. Chem. 100, 13200–13212 (1996). https://doi.org/10.1021/jp953538d

work page doi:10.1021/jp953538d 1996

[6] [6]

: The frustration-based approach of supercooled liquids and the glass transition

Tarjus, G., Kivelson, S.A., Nussinov, Z., Viot, P. : The frustration-based approach of supercooled liquids and the glass transition . J. Phys. Condens. Matter 17, R1143 –R1182 (2005). https://doi.org/10.1088/0953-8984/17/50/R01

work page doi:10.1088/0953-8984/17/50/r01 2005

[7] [7]

Adam, G., Gibbs, J.H.: On the temperature dependence of cooperative relaxation properties in glass forming liquids. J. Chem. Phys. 43, 139–146 (1965). https://doi.org/10.1063/1.1696442

work page doi:10.1063/1.1696442 1965

[8] [8]

Lubchenko, V ., Wolynes, P.G.: Theory of structural glasses and supercooled liquids. Annu. Rev. Phys. Chem. 58, 235–266 (2007). https://doi.org/10.1146/annurev.physchem.58.032806.104653

work page doi:10.1146/annurev.physchem.58.032806.104653 2007

[9] [9]

: Packing of spheres

Bernal, J.D., Mason, J. : Packing of spheres . Nature 188, 910 –911 (1960). https://doi.org/10.1038/188910a0

work page doi:10.1038/188910a0 1960

[10] [10]

Nature 453, 629–632 (2008)

Song, C., Wang, P., Makse, H.A.: A phase diagram for jammed matter. Nature 453, 629–632 (2008). https://doi.org/10.1038/nature06981

work page doi:10.1038/nature06981 2008

[11] [11]

Behringer, R.P ., Chakraborty, B.: The physics of jamming for granular materials: a review. Rep. Prog. Phys. 82(1), 012601 (2019). https://doi.org/10.1088/1361-6633/aadc3c

work page doi:10.1088/1361-6633/aadc3c 2019

[12] [12]

: Theory of powders

Edwards, S.F., Oakeshott, R.B.S. : Theory of powders . Physica A 157, 1080 –1090 (1989). https://doi.org/10.1016/0378-4371(89)90034-4

work page doi:10.1016/0378-4371(89)90034-4 1989

[13] [13]

Blumenfeld, R., Edwards, S.F.: On Granular Stress Statistics: Compactivity, Angoricity, and Some Open Issues. J. Phys. Chem. B 113, 3981–3987 (2009). https://doi.org/10.1021/jp809768y

work page doi:10.1021/jp809768y 2009

[14] [14]

: Edwards statistical mechanics for jammed granular matter

Baule, A., Morone, F., Herrmann, H.J., Makse, H.A. : Edwards statistical mechanics for jammed granular matter. Phys. Rev. Lett. 121, 188002 (2018). https://doi.org/10.1103/RevModPhys.90.015006 18

work page doi:10.1103/revmodphys.90.015006 2018

[15] [15]

Asenjo, D., Paillusson, F., Frenkel, D.: Numerical calculation of granular entropy. Phys. Rev. Lett. 112, 098002 (2014). https://doi.org/10.1103/PhysRevLett.112.098002

work page doi:10.1103/physrevlett.112.098002 2014

[16] [16]

Martiniani, S., Schrenk, K.J., Stevenson, J.D., Wales, D.J., Frenkel, D.: Turning intractable counting into sampling: Computing the configurational entropy of three -dimensional jammed packings . Phys. Rev. E 93, 012906 (2016). https://doi.org/10.1103/PhysRevE.93.012906

work page doi:10.1103/physreve.93.012906 2016

[17] [17]

: An equation of state for granular media at isotropic compression

Oquendo, W.F., Muñoz, J., Radjai, F. : An equation of state for granular media at isotropic compression. Europhys. Lett. 114, 14004 (2016). https://doi.org/10.1209/0295-5075/114/14004

work page doi:10.1209/0295-5075/114/14004 2016

[18] [18]

Ai, X., Yuan, H., Zhang, S., Zeng, Z., Li, H., Xia, C., Wang, Y .: Testing Adam–Gibbs relationship in tapped granular packings. Commun. Phys. 8, 157 (2025). https://doi.org/10.1038/s42005-025-02070- 9

work page doi:10.1038/s42005-025-02070- 2025

[19] [19]

Solid State Ionics 209–210, 1–4 (2012)

Papathanassiou, A.N., Sakellis, I., Grammatikakis, J.: Dielectric relaxation in granular dielectrics. Solid State Ionics 209–210, 1–4 (2012). https://doi.org/10.1016/j.ssi.2011.12.011

work page doi:10.1016/j.ssi.2011.12.011 2012

[20] [20]

Macromolecules 55, 7614–7625 (2022)

Shafqat, N., Alegría, A., Arbe, A., Malicki, N., Dronet, S., Porcar, L., Colmenero, J.: Disentangling the calorimetric glass -transition trace in polymer/oligomer mixtures from the modeling of dielectric relaxation and the input of small -angle neutron scattering . Macromolecules 55, 7614–7625 (2022). https://doi.org/10.1021/acs.macromol.2c0060

work page doi:10.1021/acs.macromol.2c0060 2022

[21] [21]

Wang, Y .: Granular packing as model glass formers . Chin. Phys. B 26, 014503 (2017). https://doi.org/10.1088/1674-1056/26/1/014503

work page doi:10.1088/1674-1056/26/1/014503 2017

[22] [22]

Xia, Y ., Li, J., Cao, Y ., Kou, B., Xiao, X., Fezza, K., Xiao, T., Wang, Y .: The structural origin of the hard-sphere glass transition in granular packing . Nat. Commun. 6, 8409 (2015). https://doi.org/10.1038/ncomms9409

work page doi:10.1038/ncomms9409 2015

[23] [23]

Physica A 296, 451–459 (2001)

Coniglio, A., Nicodemi, M.: A statistical mechanics approach to inherent states of granular media. Physica A 296, 451–459 (2001). https://doi.org/10.1016/S0378-4371(01)00190-X

work page doi:10.1016/s0378-4371(01)00190-x 2001

[24] [24]

Aste, T., Di Matteo, T.: Emergence of Gamma distributions in granular materials. Phys. Rev. E 77, 021309 (2008). https://doi.org/10.1103/PhysRevE.77.021309

work page doi:10.1103/physreve.77.021309 2008

[25] [25]

Taylor & Francis, London (2008)

Aste, T., Weaire, D.: The Pursuit of Perfect Packing. Taylor & Francis, London (2008)

work page 2008

[26] [26]

: Hopping conductivity in granular metals

Sheng, P. : Hopping conductivity in granular metals . Phys. Rev. Lett. 31, 44 –47 (1973). https://doi.org/10.1103/PhysRevLett.31.44

work page doi:10.1103/physrevlett.31.44 1973