# Charge-current correlation equalities for quantum systems far from equilibrium

## TL;DR

This paper extends the validity of a correlation equality between conserved charges and currents in quantum systems far from equilibrium, showing it holds under broader conditions including non-translation invariant lattice models and any space dimension.

## Contribution

It generalizes a previously derived correlation equality, demonstrating its applicability in more diverse non-equilibrium quantum systems.

## Key findings

- Correlation equality holds without translation invariance.
- Correlation identities imply symmetry in non-equilibrium linear response.
- Results apply to lattice models in any space dimension.

## Abstract

We prove that a recently derived correlation equality between conserved charges and their associated conserved currents for quantum systems far from equilibrium [O.A. Castro-Alvaredo et al., Phys. Rev. X \textbf{6}, 041065 (2016)], is valid under more general conditions than assumed so far. Similar correlation identities, which in generalized Gibbs ensembles give rise to a current symmetry somewhat reminiscent of the Onsager relations, turn out to hold also in the absence of translation invariance, for lattice models, and in any space dimension, and to imply a symmetry of the non-equilibrium linear response functions.