Feldmann Tova, Kosloff Ronnie
Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):016101. doi: 10.1103/PhysRevE.68.016101. Epub 2003 Jul 3.
The fundamentals of a quantum heat engine are derived from first principles. The study is based on the equation of motion of a minimum set of operators, which is then used to define the state of the system. The relation between the quantum framework and the thermodynamical observables is examined. A four-stroke heat engine model with a coupled two-level system as a working fluid is used to explore the fundamental relations. In the model used, the internal Hamiltonian does not commute with the external control field, which defines the two adiabatic branches. Heat is transferred to the working fluid by coupling to hot and cold reservoirs under constant field values. Explicit quantum equations of motion for the relevant observables are derived on all branches. The dynamics on the heat transfer constant field branches is solved in closed form. On the adiabats, a general numerical solution is used and compared with a particular analytic solution. These solutions are combined to construct the cycle of operation. The engine is then analyzed in terms of the frequency-entropy and entropy-temperature graphs. The irreversible nature of the engine is the result of finite heat transfer rates and frictionlike behavior due to noncommutability of the internal and external Hamiltonians.
量子热机的基本原理是从第一性原理推导出来的。该研究基于一组最小算符的运动方程，然后用其定义系统的状态。研究了量子框架与热力学可观测量之间的关系。采用一个以耦合二能级系统作为工作流体的四冲程热机模型来探究基本关系。在所使用的模型中，内部哈密顿量与外部控制场不对易，外部控制场定义了两个绝热分支。在恒定场值下，通过与热库和冷库耦合，热量传递给工作流体。在所有分支上推导了相关可观测量的显式量子运动方程。求解了传热恒定场分支上的动力学的封闭形式解。在绝热线上，采用一般数值解并与一个特定解析解进行比较。将这些解结合起来构建操作循环。然后根据频率 - 熵图和熵 - 温度图对热机进行分析。热机的不可逆性是有限传热速率以及由于内部和外部哈密顿量不对易导致的类似摩擦行为的结果。
