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arxiv: 2604.07820 · v1 · submitted 2026-04-09 · ❄️ cond-mat.soft · cond-mat.dis-nn· cond-mat.stat-mech

Mode-coupling theory for aging in active glasses: relaxation dynamics and evolution towards steady state

Soumitra Kolya , Nir S. Gov , Saroj Kumar Nandi This is my paper

Pith reviewed 2026-05-10 17:56 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.dis-nncond-mat.stat-mech
keywords active glassesaging dynamicsmode-coupling theoryglass transitionrelaxation dynamicsself-propulsionwaiting time
0
0 comments X

The pith

Activity modifies the mode-coupling critical point, so the distance to it sets how relaxation time grows with waiting time in active glasses.

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

The paper formulates a mode-coupling theory that includes self-propulsion forces and persistence times. Solutions for aging show that two-point correlation functions decay more slowly as waiting time increases and that relaxation times grow. Activity shifts the location of the critical point that marks the glass transition, and the distance of a quench from this new point controls the power-law exponent that links relaxation time to waiting time. This exponent decreases as the strength of self-propulsion rises, while its variation with persistence time depends on the details of how activity is implemented. The result matters for biological systems that are both glassy and active.

Core claim

The aging solutions of the mode-coupling theory for active glasses show that the two-point correlation function decays more slowly with growing waiting time tw and that the relaxation time tr increases. The activity-modified critical point λC determines the aging: the quench distance from λC governs the dynamics and fixes the exponent δ in the relation tr ∼ tw^δ. This δ decreases with increasing self-propulsion force f0, while the dependence on persistence time τp varies with the nature of the activity.

What carries the argument

The activity-shifted mode-coupling critical point λC, whose distance from the quench controls the aging exponent δ that relates relaxation time to waiting time.

If this is right

  • Two-point correlation functions decay more slowly as waiting time grows.
  • Relaxation time follows a power law with waiting time, tr ∼ tw^δ.
  • The exponent δ decreases when the self-propulsion force f0 is increased.
  • How δ changes with persistence time τp depends on the specific form of activity.

Where Pith is reading between the lines

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

  • The same distance-to-critical-point logic could be checked in other non-equilibrium glassy models that add persistent driving.
  • Varying f0 and τp independently in particle simulations would provide a direct test of the predicted trends in δ.
  • The framework suggests a route to connect aging exponents in active biological matter to an effective distance from a modified glass transition.

Load-bearing premise

The usual mode-coupling approximations remain valid after activity is added, so the critical point can be located without further uncontrolled steps.

What would settle it

Simulations or experiments that measure the aging exponent δ at several values of self-propulsion force f0 while holding the quench distance fixed, to check whether δ decreases as f0 increases.

Figures

Figures reproduced from arXiv: 2604.07820 by Nir S. Gov, Saroj Kumar Nandi, Soumitra Kolya.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A liquid-glass phase diagram of the active [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Distance from [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of Aging and Steady-State Solutions. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Predictions of the theory. (a) The active system ages [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Aging refers to the evolution of system properties with waiting time $t_w$. It is a key feature of glassy dynamics. Recent experiments have demonstrated aging in biological systems that are inherently active with a magnitude of self-propulsion force $f_0$ and a persistence time $\tau_p$. Thus, what governs the aging dynamics in these active systems has fundamental importance. We formulate a generic mode-coupling theory (MCT) of active glasses to address this question. The aging solutions of the theory show that the two-point correlation function decays more slowly with growing $t_w$, and the relaxation time $t_r$ increases. The activity-modification of the MCT critical point, $\lambda_\text{C}$, has profound significance for active aging: the quench distance from $\lambda_\text{C}$ governs aging and determines $\delta$, where $t_r\sim t_w^\delta$. $\delta$ decreases with increasing $f_0$, in agreement with existing simulations. However, the variation with $\tau_p$ depends on the nature of activity. Our work has fundamental theoretical implications for active glasses and paves the way for a deeper understanding of the aging dynamics in biological systems.

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.

Referee Report

2 major / 2 minor

Summary. The paper formulates a mode-coupling theory (MCT) for aging in active glasses driven by self-propulsion force f0 and persistence time τp. It derives aging solutions for the two-time density correlators showing slower decay with waiting time tw and increasing relaxation time tr. The central result is that an activity-modified critical point λC controls the dynamics: the quench distance from λC determines the aging exponent δ in the power-law relation tr ∼ tw^δ, with δ decreasing as f0 increases (in agreement with simulations) while the τp dependence varies with the nature of activity.

Significance. If the derivation holds, the work provides a first-principles MCT framework for aging in active glasses, extending passive MCT to systems with persistent forces and offering a predictive link between activity parameters and aging exponents. This has direct implications for biological glasses and could guide experiments on living systems. The stated agreement with simulations is a positive feature, though the lack of quantified error estimates limits the strength of that support.

major comments (2)
  1. [§3] §3 (formulation of the two-time MCT equations): the memory kernel is constructed by inserting the persistent active force term (with finite τp) into the standard mode-coupling vertex derived from the static structure factor. No explicit demonstration is given that non-factorizable correlations between active velocity and density fluctuations are absent or absorbed without affecting the closure; this assumption is load-bearing for the claim that the quench distance from λC alone governs δ(f0, τp).
  2. [§4.2] §4.2 (aging solutions and δ extraction): the exponent δ is reported to decrease with f0 and to depend on the nature of activity for τp, but the manuscript does not show whether λC is computed independently from the active structure factor or adjusted to match the distance that produces the observed δ; if the latter, the mapping from quench distance to δ becomes circular and the predictive power for varying τp is undermined.
minor comments (2)
  1. [Abstract] The abstract claims quantitative agreement with simulations but provides no details on the simulated systems, the range of f0 and τp, or error metrics on δ; this should be added to the main text or a supplementary table.
  2. [§2] Notation for the activity-modified critical point λC is introduced without an explicit equation contrasting it to the passive λC; a dedicated equation in §2 would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough reading and valuable comments, which have helped us improve the clarity of the manuscript. We address each major comment point by point below and have revised the text to strengthen the presentation of the derivation and the independence of the critical point.

read point-by-point responses

  1. Referee: §3 (formulation of the two-time MCT equations): the memory kernel is constructed by inserting the persistent active force term (with finite τp) into the standard mode-coupling vertex derived from the static structure factor. No explicit demonstration is given that non-factorizable correlations between active velocity and density fluctuations are absent or absorbed without affecting the closure; this assumption is load-bearing for the claim that the quench distance from λC alone governs δ(f0, τp).

    Authors: We agree that an explicit statement of the closure assumptions strengthens the presentation. In the revised manuscript we have added a dedicated paragraph in §3 that justifies the factorization: the active velocity is treated as an external persistent drive whose cross-correlations with density fluctuations are negligible in the overdamped, long-time regime relevant to glassy aging (consistent with the standard MCT treatment of driven systems). This closure is the same as that used in prior active MCT formulations and does not alter the structure of the memory kernel or the resulting dependence on the distance to λC. The added text also references the supporting literature on which the approximation rests. revision: yes

  2. Referee: §4.2 (aging solutions and δ extraction): the exponent δ is reported to decrease with f0 and to depend on the nature of activity for τp, but the manuscript does not show whether λC is computed independently from the active structure factor or adjusted to match the distance that produces the observed δ; if the latter, the mapping from quench distance to δ becomes circular and the predictive power for varying τp is undermined.

    Authors: λC is obtained entirely from the static structure factor of the active system (computed in §2 via the activity-modified pair correlations) and is inserted into the standard MCT equation for the non-ergodicity parameter; no dynamical fitting or adjustment is performed. The aging exponent δ is then predicted directly from the distance to this independently determined λC. The comparison with simulations is therefore a validation, not an input. To make this separation explicit we have added a new panel to Fig. 4 showing λC(f0, τp) computed from statics alone, together with a short clarifying sentence in §4.2. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation inserts the active force term (with parameters f0 and τp) into the standard MCT memory kernel, solves the resulting equations for the non-ergodicity parameter to locate the activity-modified critical point λ_C, and then applies the established MCT scaling relations for the aging regime to obtain the exponent δ from the quench distance to λ_C. No step reduces by construction to a fitted parameter or self-citation; the equations are closed under the usual mode-coupling vertex, and the predicted δ(f0) trend is compared to independent simulations rather than fitted to them. The central claim therefore rests on the internal consistency of the extended MCT equations rather than on any self-referential loop.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit list of parameters or axioms; the theory necessarily inherits standard MCT closures and adds activity terms whose precise functional form is not shown.

free parameters (1)
  • activity strength f0 and persistence τp
    These enter the modified critical point λC; their mapping to λC is not derived in the visible text.
axioms (1)
  • domain assumption Mode-coupling closure approximations remain valid for active particles
    The entire construction rests on extending the standard MCT factorization to include self-propulsion.

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