SciPost Submission Page
Prethermal inverse Mpemba effect
by Koudai Sugimoto, Tomotaka Kuwahara, Keiji Saito
Submission summary
| Authors (as registered SciPost users): | Koudai Sugimoto |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202511_00068v1 (pdf) |
| Date submitted: | Nov. 26, 2025, 10:11 a.m. |
| Submitted by: | Koudai Sugimoto |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
We used ChatGPT (GPT-5.1) to proofread the final manuscript.
Abstract
The inverse Mpemba effect is a counterintuitive phenomenon in which a system, initially in thermal equilibrium and prepared at different temperatures below that of the final equilibrium state, relaxes to the final state more rapidly when starting from a lower initial temperature. We extend this concept to the relaxation toward a prethermal state in driven isolated quantum systems. By examining a simple model that exhibits prethermalization, we demonstrate that this effect indeed manifests under periodic driving. We further discuss the realization of this phenomenon in a variety of systems within a unified theoretical framework.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
- Investigates novel relaxation behaviours in a new setting, namely relaxation toward a pre-thermal or meta stable state
Weaknesses
- The tools which are used to analyse the effect do not seem to be the most effective probe of the behaviour -The results of the analysis do not clearly show the novel behaviour described
Report
While the extension of Mpemba physics to study relaxation to prethermal and metastable states is a novel one, the means of analysis and the final results are not convincing. Thus I cannot recommend publication without the referees addressing the comments and questions below.
-I think the discussion surrounding the definition of the IME and its pre-thermal version requires improvement. The authors define an IME based on a time scale which is set by an energy density being close to the final energy density. Since they consider a non-equilibrium and driven process process in a quantum system they should clarify what they mean by energy density and how it should be defined in such a setting and why it relates to relaxation to a pre-thermal state. Also, it is not clear if this definition appears in this paper for the first time or has appeared elsewhere.
-In recent years many probes of Mpemba effects have been introduced but these mostly consider the distances between the density matrix of the system and its stationary value. These probes often have nice properties for example if the distance between the states vanishes then the states are the same. It is not clear if the same properties hold for their quantity. For example, if the energy densities are the same what does that say about the states themselves? Are they close in any way?
- The sketch of the effect in Figure one makes it clear what the authors intend. A two stage relaxation process with crossings occurring between different initial states. In the final results however it is not clear to me that there is a two stage relaxation process. They state that in figure 2(b) the energy densities depicted in the coloured curves "clearly" differ from the infinite temperature value plotted using the dashed black line. I don't think one can say this is clear at all. These are numerical curves at finite size and in fact can be tuned to lie either side of the dashed line by changing \beta^{-1}. Some further justification/clarification of these statements should be made. Furthermore it would be nice for the authors to comment on the fact that the energy density can be above the infinite temperature state.
-The authors also consider the IPR plotted in figures 2 and 3. This quantity also does not show a clear two step relaxation. Moreover, the crossing is not witnessed in this quantity, thus the two quantities appear to be in tension. Can the authors comment on this.
Requested changes
-Add references to the literature on pre-thermalization and pre-relaxation in the introduction - Add discussion on the definitions of the IME and the use of energy densities in a driven system -Comment on the two stage relaxation -Comment on the apparent tension between the energy density and IPR
Recommendation
Ask for major revision