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Ballistic macroscopic fluctuation theory via mapping to point particles
by Jitendra Kethepalli, Andrew Urilyon, Tridib Sadhu, Jacopo De Nardis
Submission summary
| Authors (as registered SciPost users): | Jitendra Kethepalli |
| Submission information | |
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| Preprint Link: | scipost_202506_00014v1 (pdf) |
| Date submitted: | June 6, 2025, 12:17 p.m. |
| Submitted by: | Jitendra Kethepalli |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
{\bf Ballistic Macroscopic Fluctuation Theory (BMFT) captures the evolution of fluctuations and correlations in systems where transport is strictly ballistic. We show that, for \emph{generic integrable models}, BMFT can be constructed through a direct mapping onto ensembles of classical or quantum point particles. This mapping generalises the well-known correspondence between hard spheres and point particles: the two-body \emph{scattering shift} now plays the role of an effective rod length for arbitrary interactions. Within this framework we re-derive both the full-counting statistics and the long-range correlation functions previously obtained by other means, thereby providing a unified derivation. Our results corroborate the general picture that all late-time fluctuations and correlations stem from the initial noise, subsequently convected by Euler-scale hydrodynamics. }
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The authors use a generalized hard rod mapping to express asymptotic quasi-particle trajectories in integrable systems to those of non-interacting particles. These facilitate a straightforward computation of large fluctuations and correlations after reversing the mapping from non-interacting to interacting particles.
Some comments and questions:
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It is not clear whether the central equations 5 and 9 of the generalized hard rod transformation are simply postulated or whether they refer to previous work (specifically ref. 69, 70 being a detailed investigation of a particular example).
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The paper is at times difficult to follow due to extensive derivations and equations in the main text, e.g. BMFT of point particles in section 2, and two-point correlations on section 5, the majority of which could be moved to the appendix while preserving the main message of the paper.
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What is a "typical equilibrium profile" mentioned in 26? I could not find a statement as to how it is characterized. This also brings me to a conceptual problem - In eq. 21 the large deviations function is expressed as an average over a "typical" phase space density while large deviations invariable result from "atypical" initial configurations. How is this reconciled?
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Section 3: "... we have assumed that the statistical nature of the initial profile, when described in the point particle density ..., is governed by the probability density functional with the large deviation function..."
What precisely does this assumption encompass?
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In Figure 4 the deviations from Gaussianity are appreciable only for the smallest time (T=10). Presumably this is due to direct sampling of large values becoming exponentially hard with time. On the other hand, it is not clear from the presented data what part of this is due to finite-time effects. In principle large deviations can be sampled efficiently by tilting the measure.
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The identification of cumulants and correlators with derivatives of the asymptotic form of the their respective generating functions in eqs. 82, 95 123 requires additional regularity assumptions, see e.g. Ž Krajnik, J Schmidt, V Pasquier, E Ilievski, T Prosen Physical Review Letters 128 (16), 160601. This is more than a technical detail as the regularity condition is known to be violated in a number of integrable models.
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In the Conclusions, the authors claim that the method can be applied to "generic" and "arbitrary" integrable models. At the moment this does not seem to be the case for classical integrable models. For example eq. 29 gives the free energy of classical particles which is correct but incomplete whereas 142 refers to classical systems which is wrong.
Specifically, it is known that description of certain classical integrable models involve radiative modes nor can solitons always be treated as classical particles, see e.g.:
A Bastianello, B Doyon, GMT Watts, T Yoshimura SciPost Physics 4 (6), 045 R Koch, JS Caux, A Bastianello Journal of Physics A: Mathematical and Theoretical 55 (13), 134001 A Bastianello, Ž Krajnik, E Ilievski Physical Review Letters 133 (10), 107102
To the best of my knowledge, a derivation of generalized hydrodynamics from kinetics of a generic classical integrable systems remains an open problem precisely because of this difficulty.
Minor comments/typos:
page 3: hard rods gas -> hard rod gas page 5: in the express ... in the normal mode density (?) eqs 1, 14 and others: the order of integrals over x and theta changes sporadically Appendices: Hard rods -> hard rods In 1.2 after eq. 14 the free coordinates (X, k) are mentioned, but it is unclear what k is from the surrounding explanation.
Overall, the work explores a natural idea to quantify dynamics of quasi-particles within a hydrodynamic framework and uses it to recover some previously obtained results. However, as noted above, some points require further clarification and it is not clear how different the method is from related hydrodynamic techniques used in the field.
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