SciPost Submission Page
Quantum chaos and the arrow of time
by Nilakash Sorokhaibam
Submission summary
| Authors (as registered SciPost users): | Nilakash Sorokhaibam |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2212.03914v10 (pdf) |
| Date submitted: | May 7, 2025, 4:42 p.m. |
| Submitted by: | Sorokhaibam, Nilakash |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
We show that quantum chaotic many-body systems possess the thermodynamic arrow of time in the thermodynamic limit. Berry's conjecture in quantum chaotic systems and equivalence of ensembles imply the Kelvin statement of the second law of thermodynamics at leading order in perturbation theory. We verify this result using numerical calculations. We also show that this gives rise to new constraints on the off-diagonal terms in eigenstate thermalization hypothesis (ETH) statement. We call the new constraints collectively as ETH-monotonicity. These constraints arise because pure entropic consideration is not enough for the emergence of the thermodynamic arrow of time.
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
Author comments upon resubmission
List of changes
(1) Extensive changes have been made in the manuscript. It has grown from 12 pages to 30 pages. So, let me refrain from listing all the minute changes made.
(2) The results have been fine-tuned and made precise.
(4) Detailed mathematical derivations and arguments of some of the main results have been added.
(3) The peak of the entropic factor (as pointed out by the referee 3) has been studied in detail. The peak does not play any significant role in large systems.
(2) The results have been fine-tuned and made precise.
(4) Detailed mathematical derivations and arguments of some of the main results have been added.
(3) The peak of the entropic factor (as pointed out by the referee 3) has been studied in detail. The peak does not play any significant role in large systems.
Current status:
In refereeing
Reports on this Submission
Report
This paper claims to show that an arrow of time arises naturally in quantum chaotic systems. The argument begins with the claim that, in a many-body quantum chaotic system, a generic time-dependent perturbation (which occurs over a finite time) will cause a change in energy ΔE that has the same sign as the temperature T. The author then invokes the thermodynamic relation ΔE = T ΔS to argue that ΔS is always positive, and then invokes the second law of thermodynamics to argue that this shows the existence of an arrow of time.
In my view, this is a circular argument, because the arrow of time that is implied by the the second law is assumed rather than proved. Relatedly, the author does not provide a dynamic definition of entropy as a quantity that could be computed given the quantum state (pure or mixed). My opinion is that this is a fundamental flaw in the paper.
In my view, this is a circular argument, because the arrow of time that is implied by the the second law is assumed rather than proved. Relatedly, the author does not provide a dynamic definition of entropy as a quantity that could be computed given the quantum state (pure or mixed). My opinion is that this is a fundamental flaw in the paper.
Recommendation
Reject
Author: Nilakash Sorokhaibam on 2025-05-22 [id 5506]
(in reply to Report 2 on 2025-05-21)Dear referee,
Thank you for the report. We think you missed a few points which we want to point out.
(1) We do not need the thermodynamic relation $\Delta E=T\Delta S$. We do not need a definition of entropy because we are working with the Kelvin statement of the second law of thermodynamics.
(2) Our result that $\Delta E_{\beta}$ in equation (11) has the same sign as $\beta$ is a *mathematical identity*. It does not come from Berry's conjecture.
Interestingly, although not necessary for our work, it also does not define the thermal density matrix. There are infinitely many "passive" density matrices which have the same property.
We request you to elaborate why you view our result as a circular argument.
regards,
NS