Ballistic macroscopic fluctuation theory

TL;DR

This paper develops a universal ballistic macroscopic fluctuation theory (BMFT) for many-body systems, revealing long-range correlations and fluctuation symmetries at the Euler hydrodynamic scale, supported by numerical and analytical validation.

Contribution

It introduces the BMFT framework adapting macroscopic fluctuation theory to ballistic transport systems, linking fluctuations directly to Euler hydrodynamics data.

Findings

Long-range correlations develop from inhomogeneous initial states.

Gallavotti-Cohen fluctuation theorem applies at the Euler scale.

Numerical simulations confirm analytical predictions.

Abstract

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.