# Energetic footprints of irreversibility in the quantum regime

## TL;DR

This paper investigates the energetic and entropic effects of quantum irreversibility, particularly decoherence, on work extraction and heat dissipation in quantum thermodynamic processes, highlighting differences from classical irreversibility.

## Contribution

It introduces a quantum trajectory framework to distinguish quantum from classical heat footprints and quantifies how decoherence impacts work extraction.

## Key findings

- Quantum irreversibility causes a distinct heat footprint compared to classical processes.
- Decoherence reduces the maximum extractable work from quantum states with coherences.
- Quantum irreversibility involves both entropic and energetic footprints affecting thermodynamic optimization.

## Abstract

In classical thermodynamic processes the unavoidable presence of irreversibility, quantified by the entropy production, carries two energetic footprints: the reduction of extractable work from the optimal, reversible case, and the generation of a surplus of heat that is irreversibly dissipated to the environment. Recently it has been shown that in the quantum regime an additional quantum irreversibility occurs that is linked to decoherence into the energy basis. Here we employ quantum trajectories to construct distributions for classical heat and quantum heat exchanges, and show that the heat footprint of quantum irreversibility differs markedly from the classical case. We also quantify how quantum irreversibility reduces the amount of work that can be extracted from a state with coherences. Our results show that decoherence leads to both entropic and energetic footprints which both play an important role in the optimization of controlled quantum operations at low temperature.