ON THE CLASSICAL LIMIT OF QUANTUM THERMODYNAMICS IN FINITE-TIME
ON THE CLASSICAL LIMIT OF QUANTUM THERMODYNAMICS IN FINITE-TIME
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DOI：
10.1063/1.463909
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发表时间：
1992-09-15
影响因子：
4.4
通讯作者：
KOSLOFF, R
中科院分区：
文献类型：
--
作者：
GEVA, E;KOSLOFF, R
量子热机的有限时间性能已被研究，重点是经典的，高温，限制。两个基本的发动机模型进行了研究，不同的工作流体的一致性：谐波发动机，由非相互作用的谐振子，和自旋j发动机，由非相互作用的自旋j子系统。这两个模型代表了两种不同类型的引擎，有界与无界的哈密顿算子，以及费米子与玻色子类型的创造和湮灭算子。分析是基于热力学第一和第二定律的时间导数。利用量子观测量与热力学量之间的显式关系。发动机的动力学模型的半群方法。发动机优化方面的各种目标函数：功率，熵产生，和效率，同时受到有限的周期持续时间。优化的主要策略是基于欧拉-拉格朗日方程，并且类似于Salamon和Nitzan以前用于研究牛顿发动机的策略[J. Chem. Phys. 74，3546（1981）]。在经典极限下得到的最优循环不是Curzon-Ahlborn型的，即，沿着热支路的内部温度不是恒定的。这一结果与牛顿热力学相矛盾，牛顿热力学的最佳循环是Curzon-Ahlborn型的。尽管如此，牛顿热力学的一些主要特征，如最大功率下的Curzon-Ahlborn效率，在经典极限下重现。这使得建立“热力学对应原理”成为可能。“这一原理断言，唯象牛顿热力学方法提供了基于更基本的半群量子方法的理论的渐近线。有人认为，牛顿热力学的渐近性质是双重的，因为它的有效性受到两个要求的限制：高温和接近平衡。
The finite time performance of quantum heat engines has been examined with emphasis on the classical, high temperature, limit. Two basic engine models were studied, differing by their consistency of working fluid: the harmonic engine, consisting of noninteracting harmonic oscillators, and the spin-j engine, consisting of noninteracting spin-j subsystems. The two models represent two distinct types of engines, with bounded vs unbounded Hamiltonians, and with creation and annihilation operators of the Fermionic vs the Bosonic type. The analysis is based on the time derivatives of the first and second laws of thermodynamics. Explicit relations linking quantum observables to thermodynamic quantities are utilized. The dynamics of the engines was modeled by the semigroup approach. The engines were optimized with respect to various target functions: power, entropy production, and efficiency, while subject to finite cycle duration. The main strategy of optimization was based on the Euler-Lagrange equation, and is similar to that previously applied by Salamon and Nitzan for the investigation of Newtonian engines [J. Chem. Phys. 74, 3546 (1981)]. The optimal cycles obtained at the classical limit are not of the Curzon-Ahlborn type, i.e., the internal temperature along the thermal branches is not constant. This result is in conflict with Newtonian thermodynamics, where the optimal cycles are of the Curzon-Ahlborn type. Nonetheless, some of the main features of Newtonian thermodynamics, such as the Curzon-Ahlborn efficiency at maximum power, are reproduced at the classical limit. This makes it possible to establish a "thermodynamic correspondence principle." This principle asserts that the phenomenological Newtonian thermodynamic approach provides an asymptote of a theory based upon the more fundamental semigroup quantum approach. It is argued that the asymptotic nature of Newtonian thermodynamics is twofold since its validity is restricted by two demands: that of high temperatures and that of proximity to equilibrium.