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Ballistic macroscopic fluctuation theory

by Benjamin Doyon, Gabriele Perfetto, Tomohiro Sasamoto, Takato Yoshimura

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Authors (as registered SciPost users): Gabriele Perfetto · Takato Yoshimura
Submission information
Preprint Link:  (pdf)
Date submitted: 2022-11-30 11:48
Submitted by: Yoshimura, Takato
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We introduce a new universal framework describing fluctuations and correlations in quantum and classical many-body systems, at the Euler hydrodynamic scale of space and time. The framework adapts the ideas of the conventional macroscopic fluctuation theory (MFT) to systems that support ballistic transport. The resulting "ballistic MFT" (BMFT) is solely based on the Euler hydrodynamics data of the many-body system. Within this framework, mesoscopic observables are classical random variables depending only on the fluctuating conserved densities, and Euler-scale fluctuations are obtained by deterministically transporting thermodynamic fluctuations via the Euler hydrodynamics. Using the BMFT, we show that long-range correlations in space generically develop over time from long-wavelength inhomogeneous initial states in interacting models. This result, which we verify by numerical calculations, challenges the long-held paradigm that at the Euler scale, fluid cells may be considered uncorrelated. We also show that the Gallavotti-Cohen fluctuation theorem for non-equilibrium ballistic transport follows purely from time-reversal invariance of the Euler hydrodynamics. We check the validity of the BMFT by applying it to integrable systems, and in particular the hard-rod gas, with extensive simulations that confirm our analytical results.

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Has been resubmitted

Reports on this Submission

Anonymous Report 1 on 2023-2-3 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2206.14167v3, delivered 2023-02-03, doi: 10.21468/SciPost.Report.6667


The paper develops a formalism for describing macroscopic fluctuations for the hydrodynamics of an arbitrary number of conserved quantities which possess ballistic modes. The main output of the approach is a formal setup for computing the full counting statistics of charges and currents, and dynamical correlation functions, both in the presence of a slowly space-dependent initial Gibbs ensemble. These quantities are then computed explicitly in the case of integrable systems.

Determining the general structures governing the emergent dynamics of many-body systems, classical and quantum, is presently a very active area of research. The paper is quite well-written and certainly contains results that can lead to further research on the topic. I therefore recommend the paper for publication, after the following remarks/questions have been addressed:

1. This formalism strongly resembles the MSR approach to fluctuating hydrodynamics, which also uses an action formulation. What are the differences between this and the MSR approach, and what are the advantages of the present framework?

2. The presence of non-local correlations in the Euler scaling limit is quite intriguing. Three- and higher-point functions should include the same type of information. Is the advantage of the BMFT in that it allows to infer this scaling somehow more systematically? Also, how are diffusive/noisy corrections expected to alter the result?

3. The authors mention that non-local correlations require the presence of multiple conserved quantities. I'm confused by this statement: one can have a ballistic hydrodynamic mode with only a single conserved charge (at the cost of breaking time reversal), wouldn't such systems also possess non-local correlations in the same scaling limit?

Finally, there is a minor typo on p. 29 above eq. (84): "T(o1)T(o1)" -> "T(o1)T(o2)".

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