# Transport fluctuations in integrable models out of equilibrium

## TL;DR

This paper derives exact formulas for the full counting statistics of conserved quantities transferred in integrable models out of equilibrium, combining generalized hydrodynamics and large deviation theory, and confirms predictions through simulations.

## Contribution

It introduces a novel approach to compute full counting statistics in integrable models using generalized hydrodynamics and large deviations, applicable to various physical systems.

## Key findings

- Exact results for transfer statistics in integrable models
- Validation through Monte Carlo simulations
- Confirmation of non-equilibrium fluctuation relations

## Abstract

We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We do this by combining insights from generalised hydrodynamics with a theory of large deviations in ballistic transport. The results are applicable to a wide variety of physical systems, including the Lieb-Liniger gas and the Heisenberg chain. We confirm the predictions in non-equilibrium steady states obtained by the partitioning protocol, by comparing with Monte Carlo simulations of this protocol in the classical hard rod gas. We verify numerically that the exact results obey the correct non-equilibrium fluctuation relations with the appropriate initial conditions.