# Non-equilibrium quantum thermodynamics in Coulomb crystals

## TL;DR

This paper investigates the non-equilibrium work statistics during sudden parameter changes in ion Coulomb crystals near a structural phase transition, revealing divergence and critical behavior linked to quantum Ising models.

## Contribution

It provides an analytical and numerical analysis of irreversible work in Coulomb crystals near the linear-zigzag transition, connecting it to quantum critical phenomena.

## Key findings

- Irreversible work diverges near the transition
- Work fluctuations exhibit non-analytic behavior
- Results are experimentally verifiable with current ion trap technology

## Abstract

We present an in-depth study of the non-equilibrium statistics of the irreversible work produced during sudden quenches in proximity to the structural linear-zigzag transition of ion Coulomb crystals in 1+1 dimensions. By employing both an analytical approach based on a harmonic expansion and numerical simulations, we show the divergence of the average irreversible work in proximity to the transition. We show that the non-analytic behaviour of the work fluctuations can be characterized in terms of the critical exponents of the quantum Ising chain. Due to the technological advancements in trapped ion experiments, our results can be readily verified.