Lee Sangyun, Ha Meesoon, Jeong Hawoong
Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34051, Korea.
Department of Physics Education, Chosun University, Gwangju 61452, Korea.
Phys Rev E. 2021 Feb;103(2-1):022136. doi: 10.1103/PhysRevE.103.022136.
To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycle's productivity and precision. Interestingly, as the strength (heat conductance) between the system and the bath increases, the precision of the quantum Otto cycle overtakes that of the classical one. Testing the conventional TUR of the Otto cycle, in the region where the entropy production is large enough, we find a tighter bound than that of the conventional TUR. However, in the finite-time mode, both quantum and classical Otto cycles violate the conventional TUR in the region where the entropy production is small. This implies that another modified TUR is required to cover the finite-time Otto cycle. Finally, we discuss the possible origin of this violation in terms of the uncertainty products of the thermodynamic quantities and the relative error near resonance conditions.
为了揭示量子特性在奥托循环中的作用，并讨论热力学不确定性关系（TUR）在该循环中的有效性，我们研究了量子奥托循环及其经典对应物。特别地，我们精确计算了热力学量的平均值和相对误差。在准静态极限下，与不存在量子特性的情况相比，量子特性降低了奥托循环的效率和精度，而在有限时间模式下，它可以提高循环的效率和精度。有趣的是，随着系统与热库之间的强度（热导率）增加，量子奥托循环的精度超过了经典奥托循环。在熵产生足够大的区域测试奥托循环的传统TUR时，我们发现了一个比传统TUR更严格的界限。然而，在有限时间模式下，量子和经典奥托循环在熵产生较小的区域都违反了传统TUR。这意味着需要另一种修正的TUR来涵盖有限时间的奥托循环。最后，我们根据热力学量的不确定性乘积和共振条件附近的相对误差讨论了这种违反的可能原因。
