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arxiv: 2606.07188 · v2 · pith:YXJZZSQHnew · submitted 2026-06-05 · ❄️ cond-mat.stat-mech · quant-ph

Asymmetry dynamics and nonequilibrium symmetry-breaking phase transitions

Liv Hammer , Colin Rylands , Federico Carollo This is my paper

Pith reviewed 2026-06-27 20:43 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords quantum Mpemba effectasymmetry dynamicssymmetry breakingopen quantum systemsnonequilibrium phase transitionsquantum many-body dynamicsanomalous relaxation
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0 comments X

The pith

Open quantum many-body systems with symmetry-breaking transitions exhibit a quantum Mpemba effect from non-monotonic asymmetry evolution.

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

This paper studies the time evolution of asymmetry in open quantum many-body systems that feature symmetry-breaking phase transitions. It shows that in the symmetric phase asymmetry changes non-monotonically, which produces a quantum Mpemba effect in which a more asymmetric initial state restores symmetry faster than a less asymmetric one. In the broken-symmetry phase the system displays an imbalance between its capacity to increase asymmetry and its capacity to decrease it. These behaviors are tied to the open-system setting and do not appear in prior closed-system studies of the quantum Mpemba effect.

Core claim

In open quantum many-body systems featuring symmetry-breaking phase transitions, the asymmetry of a subsystem evolves non-monotonically in the symmetric phase, directly producing a quantum Mpemba effect, while in the broken-symmetry phase an imbalance arises between the rates at which asymmetry can increase or decrease.

What carries the argument

The asymmetry of a subsystem, used as an analog of temperature, whose non-monotonic time evolution in the symmetric phase generates the Mpemba effect and whose change rates become imbalanced in the broken phase.

If this is right

  • A quantum Mpemba effect appears in the symmetric phase as a direct result of non-monotonic asymmetry evolution.
  • An imbalance exists between the system's ability to increase versus decrease its asymmetry in the broken-symmetry phase.
  • Open quantum many-body systems with symmetry-breaking transitions serve as a platform for observing and controlling anomalous relaxation.
  • The reported behaviors extend the quantum Mpemba effect beyond closed systems to dissipative many-body settings.

Where Pith is reading between the lines

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

  • The non-monotonic asymmetry could be used to design protocols that accelerate or slow symmetry restoration in engineered open quantum systems.
  • Similar imbalance effects might appear in other dissipative models that lack an explicit phase transition but still break symmetry.
  • Numerical studies of specific lattice models with local dissipation could map the parameter regions where the Mpemba effect is strongest.

Load-bearing premise

The open quantum many-body dynamics with symmetry-breaking phase transitions permit a non-monotonic asymmetry evolution that is absent in closed-system settings.

What would settle it

A calculation or experiment on a concrete open quantum many-body model with symmetry breaking that finds strictly monotonic asymmetry decay throughout the symmetric phase would rule out the reported Mpemba effect.

Figures

Figures reproduced from arXiv: 2606.07188 by Colin Rylands, Federico Carollo, Liv Hammer.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a,b) we show the behavior of ∆S(t, ℓ), as a function of time, for initial states with different values of mx(0) and (a) mz(0) < 0, (b) mz(0) > 0. For mz(0) < 0 the REA has an overall monotonic decrease toward the sta￾tionary value and only displays small oscillations around this decay. In this regime, we observe that the more the symmetry is broken by the initial state, the longer the time it takes for it… view at source ↗
Figure 3
Figure 3. Figure 3: (a)]. Comparing the dynamics of different initial states we see that this non-monotonic behavior can also result in a quantum Mpemba effect as clearly displayed by the density plot in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

In classical settings, the Mpemba effect occurs when a hotter system cools faster than an initially colder one. In quantum systems, this effect can be reinterpreted exploiting the concept of symmetries, with the asymmetry of a subsystem playing the role of temperature. A quantum Mpemba effect arises when a more asymmetric state restores the symmetry faster than a less asymmetric one. Previous work mainly focuses on closed systems characterized by thermal equilibration and Hamiltonian symmetries. In this paper, we analyze the dynamics of asymmetry in an open quantum many-body system featuring symmetry breaking and uncover dynamical behavior that appears to be unique to these settings. In the symmetric phase, we demonstrate the existence of a quantum Mpemba effect, which emerges as a direct consequence of a non-monotonic evolution of the asymmetry. In the broken-symmetry phase, we analyze the imbalance between the system's ability to increase or to decrease its asymmetry. Our results extend the notion of quantum Mpemba effects to open quantum many-body systems exhibiting symmetry-breaking phase transitions and establish them as a platform for observing and controlling anomalous relaxation phenomena.

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 / 0 minor

Summary. The paper analyzes the dynamics of asymmetry in an open quantum many-body system with symmetry-breaking phase transitions. It reports a quantum Mpemba effect in the symmetric phase arising directly from non-monotonic asymmetry evolution, and an imbalance between the system's ability to increase versus decrease asymmetry in the broken-symmetry phase. These behaviors are presented as unique to open-system settings with symmetry breaking, extending prior closed-system studies of quantum Mpemba effects.

Significance. If the claims are supported by the (unavailable) derivations and data, the work would establish open quantum many-body systems with symmetry-breaking transitions as a platform for anomalous relaxation, including a symmetry-based Mpemba effect. The abstract positions the non-monotonic asymmetry evolution as a direct consequence of the open dynamics, which could be a substantive extension if demonstrated.

major comments (2)
  1. [Abstract] Abstract: the central claims (quantum Mpemba effect from non-monotonic asymmetry; asymmetry imbalance in the broken phase) are stated without any derivations, numerical protocols, error analysis, or explicit methods. This prevents assessment of whether the reported behaviors are actually supported by the math or simulations.
  2. [Abstract] Abstract: the assertion that the non-monotonic asymmetry evolution and resulting Mpemba effect are 'unique to these settings' (open systems with symmetry breaking) cannot be evaluated, as no comparison to closed-system cases or explicit dynamical equations are provided.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their assessment. The abstract is a concise overview; the full manuscript contains the derivations, protocols, equations, and supporting analysis. We respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claims (quantum Mpemba effect from non-monotonic asymmetry; asymmetry imbalance in the broken phase) are stated without any derivations, numerical protocols, error analysis, or explicit methods. This prevents assessment of whether the reported behaviors are actually supported by the math or simulations.

    Authors: Abstracts are summaries and do not contain full derivations or methods. The dynamical equations, numerical protocols, error analysis, and explicit methods supporting the quantum Mpemba effect and asymmetry imbalance are provided in Sections II and III of the manuscript, with additional details and figures in the appendices. These elements allow direct assessment of the claims. revision: no

  2. Referee: [Abstract] Abstract: the assertion that the non-monotonic asymmetry evolution and resulting Mpemba effect are 'unique to these settings' (open systems with symmetry breaking) cannot be evaluated, as no comparison to closed-system cases or explicit dynamical equations are provided.

    Authors: The explicit dynamical equations, including the open-system Lindblad operators that produce the non-monotonic asymmetry, appear in Section II. The uniqueness argument rests on the mechanism requiring both open dissipation and symmetry-breaking transitions, which is absent in closed Hamiltonian systems; this contrast is outlined in the introduction and conclusion with references to prior closed-system work. The abstract qualifies the claim as behavior that 'appears to be unique.' revision: no

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The provided abstract and reader's assessment describe emergent dynamical behaviors (non-monotonic asymmetry evolution producing a quantum Mpemba effect, and asymmetry imbalance in the broken phase) as arising from analysis of open quantum many-body dynamics with symmetry-breaking transitions. No load-bearing steps are indicated that reduce by construction to fitted parameters, self-definitions, or self-citation chains. The central claims are presented as consequences of the system's evolution rather than renamed inputs or ansatzes smuggled via prior work. With no quoted equations or sections exhibiting the enumerated circular patterns, the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; full text unavailable so ledger entries are limited to those directly stated or implied in the abstract. No free parameters, invented entities, or additional axioms are identifiable.

axioms (2)
  • domain assumption Asymmetry of a subsystem can serve as the quantum analogue of temperature for defining a Mpemba effect.
    Abstract states this reinterpretation is used to extend the classical effect.
  • domain assumption The system is an open quantum many-body system that exhibits symmetry-breaking phase transitions.
    This is the core physical setting in which the new dynamical behaviors are claimed.

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discussion (0)

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Reference graph

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    L. Hammer, C. Rylands, and F. Carollo, Data supporting “Asymmetry dynamics and nonequilibrium symmetry- breaking phase transitions”, Zenodo (2026). 1 SUPPLEMENTAL MATERIAL Asymmetry dynamics and nonequilibrium symmetry-breaking phase transitions Liv Hammer1, Colin Rylands 1, Federico Carollo2 1Centre for Fluid and Complex Systems, Coventry University, Cov...

    2026