Extracting work from random collisions: A model of a quantum heat engine

TL;DR

This paper models a quantum heat engine using a single-qubit system interacting with non-equilibrium and cold reservoirs via random collisions, analyzing fluctuations in work, heat, and efficiency.

Contribution

It introduces a collision model for a quantum Otto engine with non-equilibrium reservoirs, highlighting the impact of randomness on efficiency fluctuations.

Findings

Efficiency distribution lacks finite moments

Fluctuations decrease with larger hot reservoir qudits

Mean efficiency matches classical Otto engine efficiency

Abstract

We study the statistical distribution of the ergotropy and of the efficiency of a single-qubit battery ad of a single-qubit Otto engine, respectively fuelled by random collisions. The single qubit, our working fluid, is assumed to exchange energy with two reservoirs, a non-equilibrium "hot" reservoir and a zero temperature cold reservoir. The interactions between the qubit and the reservoirs is described in terms of a collision model of open system dynamics. The qubit interacts with the non-equilibrium reservoir (a large ensemble of qudits all prepared in the same pure state) via random unitary collisions and with the cold reservoir (a large ensemble of qubits in their ground state) via a partial swap. Due to the random nature of the interaction with the hot reservoir, fluctuations in ergotropy, heat, and work are present, shrinking with the size of the qudits in the hot reservoir. While the mean, "macroscopic" efficiency of the Otto engine is the same as in the case in which the hot reservoir is a thermal one, the distribution of efficiencies does not support finite moments, so that the mean of efficiencies does not coincide with the macroscopic efficiency.