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

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 fueled by random collisions. The single qubit, our working fluid, is assumed to exchange energy with two reservoirs: a nonequilibrium hot reservoir and a zero-temperature cold reservoir. The interactions between the qubit and the reservoirs are described in terms of a collision model of open system dynamics. The qubit interacts with the nonequilibrium 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.

Automated summary

This study examines the statistical distribution of ergotropy and efficiency in a single-qubit battery and a single-qubit Otto engine fueled by random collisions. The interactions between the qubit and two reservoirs are described using a collision model of open system dynamics, revealing fluctuations in ergotropy, heat, and work that decrease with the size of the qudits in the hot reservoir. Although the mean macroscopic efficiency of the Otto engine remains the same, the distribution of efficiencies does not support finite moments, resulting in a discrepancy between the mean efficiency and the macroscopic efficiency.