# Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry

## TL;DR

This paper extends the thermodynamic uncertainty relation to systems with broken time-reversal symmetry by analyzing hysteresis in current fluctuations, with applications to gases and conductors under magnetic fields.

## Contribution

It introduces a hysteretic thermodynamic uncertainty relation applicable to non-time-reversal symmetric systems, broadening the scope of fluctuation-dissipation bounds.

## Key findings

- Derived a new uncertainty relation for hysteresis in current fluctuations.
- Validated the relation with examples involving gases and magnetic conductors.
- Showed the relation holds under various symmetry-breaking conditions.

## Abstract

The thermodynamic uncertainty relation gives a lower bound on the amount of dissipation in a mesoscopic system. By considering the fluctuations in the hysteresis of the current -- the sum of the currents in the time-forward and time-reversed processes -- we extend this relation to systems with broken time-reversal symmetry, either due to the presence of odd state variables, odd driving field or due to explicit time-dependent driving that is time-reversal asymmetric. We illustrate our predictions on a dilute, weakly-interacting gas driven out of equilibrium by the slow compression of a piston and on a ballistic multi-terminal conductor with an external magnetic field.