Shaghaghi Vahid, Palma G Massimo, Benenti Giuliano
Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy.
Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy.
Phys Rev E. 2022 Mar;105(3-1):034101. doi: 10.1103/PhysRevE.105.034101.
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.
我们分别研究了由随机碰撞驱动的单量子比特电池和单量子比特奥托发动机的工作熵及效率的统计分布。单量子比特作为我们的工作介质，假定其与两个储热器交换能量：一个非平衡“热”储热器和一个零温度冷储热器。量子比特与储热器之间的相互作用通过开放系统动力学的碰撞模型来描述。量子比特通过随机酉碰撞与非平衡储热器（大量处于相同纯态的量子位集合）相互作用，并通过部分交换与冷储热器（大量处于基态的量子比特集合）相互作用。由于与热储热器相互作用的随机性，工作熵、热量和功会出现波动，且波动会随着热储热器中量子位的数量减少。虽然奥托发动机的平均“宏观”效率与热储热器为热平衡状态时的情况相同，但效率分布不支持有限矩，因此效率的平均值与宏观效率不一致。
