Chen Jin-Fu, Qiu Tian, Quan Hai-Tao
School of Physics, Peking University, Beijing 100871, China.
Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
Entropy (Basel). 2021 Nov 29;23(12):1602. doi: 10.3390/e23121602.
Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum-classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.
由卡尔德雷拉 - 莱格特模型描述的量子布朗运动，为理解量子热力学的现象和本质带来了深刻见解，特别是与经典对应物相关的量子功和热。通过采用相空间表述方法，我们研究了量子布朗运动模型中弛豫过程的热分布。在任意弛豫时间和任意摩擦系数下，都得到了热特征函数的解析结果。通过取经典极限，该结果趋近于由朗之万方程描述的经典布朗运动的热分布，这表明了热分布的量子 - 经典对应原理。我们还证明了在任意弛豫时间的涨落热满足热的交换涨落定理，其长时间极限反映了系统的完全热化。我们的研究通过两点测量证明了量子涨落热的定义。
