Liu Junjie, Segal Dvira
Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario, Canada M5S 3H6.
Phys Rev E. 2019 Jun;99(6-1):062141. doi: 10.1103/PhysRevE.99.062141.
Recently, a thermodynamic uncertainty relation (TUR) has been formulated for classical Markovian systems demonstrating trade-off between precision (current fluctuation) and cost (dissipation). Systems that violate the TUR are interesting as they overcome another trade-off relation concerning the efficiency of a heat engine, its power, and its stability (power fluctuations). Here, we analyze the root, extent, and impact on performance of TUR violations in quantum thermoelectric junctions at steady state. Considering noninteracting electrons, first we show that only the "classical" component of the current noise, arising from single-electron transfer events, follows the TUR. The remaining, "quantum" part of current noise is therefore responsible for the potential violation of the TUR in such quantum systems. Next, focusing on the resonant transport regime we determine the parameter range in which the violation of the TUR can be observed-for both voltage-biased junctions and thermoelectric engines. We illustrate our findings with exact numerical simulations of a serial double quantum dot system. Most significantly, we demonstrate that the TUR always holds in noninteracting thermoelectric generators when approaching the thermodynamic efficiency limit.
最近，已为经典马尔可夫系统建立了一种热力学不确定性关系（TUR），它表明了精度（电流涨落）和成本（耗散）之间的权衡。违反TUR的系统很有趣，因为它们克服了另一种关于热机效率、功率及其稳定性（功率涨落）的权衡关系。在此，我们分析了稳态下量子热电结中TUR违反的根源、程度及其对性能的影响。考虑非相互作用电子，首先我们表明，仅由单电子转移事件产生的电流噪声的“经典”分量遵循TUR。因此，电流噪声的其余“量子”部分是此类量子系统中潜在违反TUR的原因。接下来，聚焦于共振输运 regime，我们确定了在其中可以观察到TUR违反的参数范围——对于电压偏置结和热电发动机都是如此。我们用串联双量子点系统的精确数值模拟来说明我们的发现。最重要的是，我们证明，在接近热力学效率极限时，TUR在非相互作用热电发电机中总是成立的。
