# Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time

## TL;DR

This paper investigates how strong interactions and quantum phase transitions in finite Hubbard chains influence energy fluctuations, irreversibility, and quantum work distributions during out-of-equilibrium dynamics, with implications for quantum thermodynamics.

## Contribution

It reveals the impact of quantum phase transitions on work fluctuations and irreversibility in finite many-body systems, highlighting the role of correlations in quantum thermodynamics.

## Key findings

- Energy fluctuation statistics change across the transition.
- Irreversibility and entropy production increase near the transition.
- Quantum features in work distribution are enhanced in the Mott-insulating phase.

## Abstract

The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a non-equilibrium dynamics. By driving transient currents to oppose the precursor to metal-Mott insulator transition in a diversity of dynamical regimes, we show how increasing correlations dramatically affect the statistics of energy fluctuations and consequently the quantum work distribution of finite Hubbard chains. Statistical properties of such distributions, as its skewness, that changes dramatically across the transition, can be related to irreversibility and entropy production. Even close to adiabaticity, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong quantum features in the quantum work distribution. In the Mott-insulating phase the work fluctuation-dissipation balance gets modified, with the irreversible entropy production dominating over work fluctuations. The effect of an interaction-driven quantum-phase-transition on thermodynamics quantities and irreversibility has to be considered in the design of protocols in small scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols at quantum scale.