SciPost Submission Page
Hydrodynamics without Averaging -- a Hard Rods Study
by Friedrich Hübner
Submission summary
| Authors (as registered SciPost users): | Friedrich Hübner |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2507.17827v2 (pdf) |
| Date submitted: | Aug. 8, 2025, 12:40 p.m. |
| Submitted by: | Friedrich Hübner |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
On the example of the integrable hard rods model we study the quality of the (generalized) hydrodynamic approximation on a single coarse-grained sample. This is opposed to the traditional approach which averages over an appropriate local equilibrium state. While mathematically more ambiguous, a major advantage of the new approach is that it allows us to disentangle intrinsic diffusion from `diffusion from convection' effects. For the hard rods we find intrinsic diffusion is absent, which agrees with and clarifies recent findings. Interestingly, the results also apply to not locally thermal states, demonstrating that hydrodynamics (in this model) does not require the assumption of local equilibrium.
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
-
Timely work on an important timely question: Is the assumption of local equilibrium really necessary to describe a system by hydrodynamics?
-
Careful study of a specific classical model: hard rods
-
Interesting statistical ensembles introduced in the numerical part: Poisson (no correlations) and Ginibre (correlated) distributions of hard rods in phase space
Weaknesses
-
The paper could probably be more concise. At times, it is hard to follow the author's reasoning.
-
While the message of the paper is formulated in a way that suggests that the idea applies to any system, regardless of its integrability, the chosen example (hard rods) is integrable, and the role of integrability in all of this remains quite unclear.
Report
It provides a careful study of that question for the case of the classical hard rod gas. The conclusion is that no local generalized equilibrium assumption is needed.
I think the paper contains interesting ideas and it will motivate further works along this direction. I recommend publication in Scipost Physics after the author implements the changes below.
Requested changes
1- The introduction is very long, and not very focused. It could be more concise, and 'to-the-point'. A summary of the results would be appreciated. Also , in the first paragraph of the introduction the author seems to be talking about integrable systems since he is talking about generalized Gibbs ensembles. But then the later discussion in the introduction seems to be aimed at all systems, including non-integrable. Please clarify whether this introduction is about integrable or generic systems.
2- Sections 3.1 ,3.2,3.3,3.4 and 5.2 merely look like technical notes. Please provide a roadmap to the reader at the beginning of each subsection to explain what is the goal of the calculations
3- Please clarify whether / which conclusions of this paper hold beyond the integrable case.
4- 'Weak solution' in page 7 does not seem to be defined. Please define.
5-There are many typos ( p.2 'would be differ', p.4 'hards', p.8 'is that is that', 'corase-graining', etc). Please proofread.
Recommendation
Ask for minor revision
Strengths
Report
Recommendation
Ask for minor revision
Strengths
1) Creative approach with concrete examples 2) Detailed calculations 3) Introduces many open questions that the methods could be applicable to.
Weaknesses
1) The applicability of these methods to more complicated models might not be so straightforward.
Report
Requested changes
1) Minor typos (page 4 'jugding' instead of judging) 2) There is a missing Delta x in Eq. 26
3) In figure 3 the blank plot should be removed.
4) Under remark 9 the sentence: "If on the other hand, one is able to only measure observables averaged over many initial states, then one should use (160) instead." Is a bit unclear to me. I take it to mean that (160) captures the dynamics that emerge having averaged over the initial states. Perhaps this could be slightly reworded to clarify the difference between (8) (evolve many samples then average) vs (160) (average initial states then evolve).
5) The author points out Ginibre states as being particularly unphysical thus demonstrating the robustness of GHD. Does the author have any insight about the types of ensemble of states that are not captured by GHD?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report #1 by Anonymous (Referee 1) on 2025-10-10 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
I was checking for the typos
Report
Requested changes
Main suggestions
1) In general, it would be good to add an additional section "main results", explaining and summarizing the results of each section
2) It will be also good to announce the results and explain the logic of derivation at the beginning of each section. And more importantly trying to exactly pronounce the starting point: equations and assumptions from which the rest is derived.
For instance:
2.1) I assume that the evolution of the coarse-grained system is further captured by Eq. 8, however it was never explicitly stated. It would be good to comment on that directly when writing down equations 76-79 and also 119-120.
Specific technical points
3) It will be good to discuss what are the author's expectations in case of a general integrable systems. Does the introduced approach allow to derive (or at least guess) the generalization of Eq. 159 to the case of a generic integrable system. If not, briefly comment why.
4) The definiton of z_{\alpha,\beta,\alpha^\prime, \beta^\prime} between 85 and 86 is inaccurate or deserves explanation, because the RHS of the definition does not contain \alpha^\prime, \beta^\prime, containing instead \alpha(x_j), \beta(x_j).
5) The estimation for the number of summation terms in Eq. 87 is not clear from the text, in particular what are the summation bounds. It is also not clear why z*{α,β,α′,β′} = O(∆x), naively it looks that for different cells α,α′ the difference \hat{x}_α-\hat{x}_α′ might be of order one, which is O(1).
6) The equations 159-160 deserve better explanation, in particular, it seems that they should be complemented by an equation for G_{LR,sym} to be complete. Without such a relation, it is not clear how to use 159-160 alone for the numerical simulation.
Minor formatting
7) as a minor suggestion: it will be good to use {multline} envitonment for a multiline equuations like 159-160 (and many others). Othervise both lines get enumerated, which is not common.
Recommendation
Ask for minor revision