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arxiv: 2603.24522 · v2 · submitted 2026-03-25 · 🪐 quant-ph

A Description of the Quantum Mpemba Effect using the Steepest-Entropy-Ascent Quantum Thermodynamics Framework

Luis Enrique Rocha-Soto , Cesar Eduardo Damian-Ascencio , Adriana Salda\~na-Robles , Sergio Cano-Andrade This is my paper

Pith reviewed 2026-05-15 00:30 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum Mpemba effectsteepest-entropy-ascentquantum thermodynamicsFeshbach projectionthree-level systemdissipative relaxationmachine learning
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The pith

The steepest-entropy-ascent quantum thermodynamics framework predicts the dynamics of the quantum Mpemba effect in an isolated three-level system.

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

This paper applies the steepest-entropy-ascent quantum thermodynamics framework to model the quantum Mpemba effect, in which a system relaxes exponentially faster to a steady state when starting from a state farther from equilibrium. It treats a single three-level isolated system and reduces the description from a four-dimensional Hilbert space to three dimensions via Feshbach projection so that the results can be compared directly with existing experiments. The dissipative acceleration is controlled by a relaxation parameter that is fixed through machine learning, producing a thermodynamically consistent account of the observed exponential relaxation. A sympathetic reader would care because this supplies an explicit dynamical mechanism for a counter-intuitive non-equilibrium phenomenon at the quantum level.

Core claim

The system dynamics of the Mpemba effect are predicted within the steepest-entropy-ascent quantum thermodynamics framework considering a single constituent three-level isolated system. The system is projected from a four-dimensional Hilbert space onto a three-dimensional one using the Feshbach projection in order to compare the theoretical results with experimental data. Since the quantum Mpemba effect is characterized by a dissipative acceleration, the relaxation parameter τ_D plays a fundamental role in the dissipative dynamics predicted by the model and is determined using machine learning methods, resulting in a model that thermodynamically describes this phenomenon at the quantum level.

What carries the argument

The steepest-entropy-ascent quantum thermodynamics framework, which selects the direction of state evolution by maximizing the instantaneous rate of entropy increase, together with Feshbach projection onto a three-level subspace and a machine-learned relaxation time τ_D that sets the scale of dissipative acceleration.

If this is right

  • The framework reproduces the exponential relaxation that defines the quantum Mpemba effect for an isolated three-level system.
  • Machine learning supplies the numerical value of the relaxation parameter required to match the dissipative acceleration seen in experiments.
  • Feshbach projection permits direct comparison between the thermodynamic model and data taken on three-level physical realizations.
  • The resulting description remains thermodynamically consistent while accounting for the counter-intuitive faster relaxation from more distant initial states.

Where Pith is reading between the lines

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

  • The same combination of steepest-ascent evolution and projection could be used to predict Mpemba-like acceleration in other few-level quantum systems whose spectra are known.
  • If the machine-learned τ_D proves transferable across different level structures, the approach offers a route to parameter-light modeling of dissipative quantum processes that lack closed-form solutions.
  • Embedding a three-level system inside a larger space and then projecting down suggests a general technique for capturing effective open-system dynamics within a closed thermodynamic framework.

Load-bearing premise

The relaxation parameter τ_D obtained from machine learning accurately encodes the dissipative acceleration without any further post-hoc adjustments that would turn the description into a mere fit to data.

What would settle it

A measurement of relaxation trajectories in a three-level quantum system whose observed time scales deviate from the exponential rates obtained when the model is run with the machine-learned value of τ_D.

Figures

Figures reproduced from arXiv: 2603.24522 by Adriana Salda\~na-Robles, Cesar Eduardo Damian-Ascencio, Luis Enrique Rocha-Soto, Sergio Cano-Andrade.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic representation of the Mpemba effect [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Population dynamics of the SEAQT model with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Time evolution of the relaxation parameter, [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Energy and entropy evolution for the SEAQT [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Nonequilibrium a) heat capacity and b) free [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Energy and entropy evolution for the Lindblad [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Population dynamics of the SEAQT model with [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Nonequilibrium a) heat capacity and b) free [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Energy and entropy evolution for the SEAQT [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Multiple Mpemba initial states randomly [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Hilbert–Schmidt distance for each initial [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: State evolution of the different randomly [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: State evolution of the different randomly [PITH_FULL_IMAGE:figures/full_fig_p015_16.png] view at source ↗
read the original abstract

The quantum Mpemba effect is a phenomenon characterized by an exponential relaxation from a non-equililbrium state to a steady state. This effect was predicted with an analysis of the Liouvillian superoperator and experimentally demonstrated in a three-level system. In this work, the system dynamics of the Mpemba effect is predicted within the steepest-entropy-ascent quantum thermodynamics framework considering a single constituent three-level isolated system. The system is projected from a four-dimensional Hilbert space onto a three-dimensional one using the Feshbach projection in order to compare the theoretical results with experimental data. Since the quantum Mpemba effect is characterized by a dissipative acceleration, the relaxation parameter, $\tau_D$, plays a fundamental rol in the dissipative dynamics predicted by the model and is determined using machine learning methods, resulting in a model that thermodynamically describes this phenomenon at the quantum level.

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

1 major / 2 minor

Summary. The paper claims to predict the dynamics of the quantum Mpemba effect using the steepest-entropy-ascent quantum thermodynamics (SEA-QT) framework applied to a single three-level isolated quantum system. The system is obtained by projecting a four-dimensional Hilbert space onto three dimensions via the Feshbach projection to facilitate comparison with experimental data. The dissipative acceleration characteristic of the effect is modeled through a relaxation parameter τ_D, which is determined using machine learning methods within this thermodynamic framework.

Significance. If the result holds, the work would establish that the SEA-QT approach can thermodynamically describe the quantum Mpemba effect in an isolated few-level system, providing a variational principle-based explanation for the observed dissipative acceleration. This has potential significance for understanding non-equilibrium quantum thermodynamics and could extend to other quantum relaxation phenomena by linking them to entropy production maximization.

major comments (1)
  1. Abstract: The central claim that the dynamics 'is predicted' within the SEA-QT framework is undermined by the reliance on machine learning to determine the relaxation parameter τ_D. The abstract provides no indication that τ_D is derived from the SEA-QT equations or fixed independently of the target data; instead, it appears optimized to reproduce the observed Mpemba dynamics, which risks reducing the description to a phenomenological fit rather than a genuine prediction from the entropy-ascent principle. This is the load-bearing assumption for the 'prediction' claim.
minor comments (2)
  1. Abstract: There is a typographical error: 'non-equililbrium' should read 'non-equilibrium'.
  2. Abstract: There is a typographical error: 'rol' should read 'role'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The single major comment raises a valid point about the wording in the abstract regarding the claim of 'prediction'. We address it directly below and will make the necessary revisions.

read point-by-point responses

  1. Referee: [—] Abstract: The central claim that the dynamics 'is predicted' within the SEA-QT framework is undermined by the reliance on machine learning to determine the relaxation parameter τ_D. The abstract provides no indication that τ_D is derived from the SEA-QT equations or fixed independently of the target data; instead, it appears optimized to reproduce the observed Mpemba dynamics, which risks reducing the description to a phenomenological fit rather than a genuine prediction from the entropy-ascent principle. This is the load-bearing assumption for the 'prediction' claim.

    Authors: We agree that the abstract wording requires clarification to avoid overstating the predictive power. The SEA-QT framework supplies the variational equations that govern the steepest entropy ascent dynamics for the isolated three-level system (after Feshbach projection). However, the single scalar relaxation parameter τ_D sets the absolute time scale of dissipation and is not fixed by the SEA-QT equations alone; it must be calibrated against data. We used machine-learning optimization to determine the value of τ_D that reproduces the experimentally observed Mpemba relaxation. This yields a thermodynamically consistent description of the effect but is not an ab-initio prediction of the time scale. We will revise the abstract to replace 'is predicted' with 'is described' and explicitly state that τ_D is obtained by machine-learning fitting to the target dynamics. Corresponding clarifications will be added in the main text where the role of τ_D is introduced. These changes will align the language with the manuscript's actual contribution while preserving the central result that the SEA-QT variational principle accounts for the dissipative acceleration characteristic of the quantum Mpemba effect. revision: yes

Circularity Check

1 steps flagged

Machine-learned τ_D reduces SEA-QT 'prediction' of Mpemba dynamics to a post-hoc fit

specific steps
  1. fitted input called prediction [Abstract]
    "Since the quantum Mpemba effect is characterized by a dissipative acceleration, the relaxation parameter, τ_D, plays a fundamental rol in the dissipative dynamics predicted by the model and is determined using machine learning methods, resulting in a model that thermodynamically describes this phenomenon at the quantum level."

    The paper presents the dissipative dynamics as predicted by SEA-QT, yet the parameter τ_D that governs the acceleration is obtained via machine learning (i.e., fitted to data). Because the claimed prediction depends on this fitted value rather than being derived solely from the entropy-ascent principle or external constraints, the output is statistically forced by the input fitting step.

full rationale

The paper's central claim is that SEA-QT applied to the Feshbach-projected three-level system predicts the dissipative acceleration characterizing the quantum Mpemba effect. However, the load-bearing relaxation parameter τ_D that controls this acceleration is explicitly stated to be determined using machine learning methods. No derivation of τ_D from the SEA-QT equation of motion or from independent microscopic principles is provided; instead, its value is obtained by optimization against data. This directly matches the fitted_input_called_prediction pattern: the 'predicted' dynamics are generated only after fitting the single free parameter to the target phenomenon, rendering the agreement a calibrated reproduction rather than an ab initio thermodynamic result. The remainder of the framework (projection, entropy ascent) supplies the functional form but does not fix the rate, so the overall description reduces to the fitted input.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model rests on the SEAQT framework as a domain assumption and on a single fitted dissipation time scale; no new entities are postulated.

free parameters (1)
  • τ_D
    Relaxation parameter that controls dissipative acceleration; its value is obtained via machine learning to reproduce the Mpemba dynamics.
axioms (2)
  • domain assumption Steepest-entropy-ascent principle governs the evolution of the isolated quantum system
    Invoked as the governing framework for the dynamics in the three-level system.
  • domain assumption Feshbach projection from four-dimensional to three-dimensional Hilbert space preserves the essential physics
    Used to enable direct comparison with experimental three-level data.

pith-pipeline@v0.9.0 · 5468 in / 1355 out tokens · 29852 ms · 2026-05-15T00:30:24.596724+00:00 · methodology

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Reference graph

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