Pal P S, Lahiri Sourabh, Jayannavar A M
Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India.
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India.
Phys Rev E. 2017 Apr;95(4-1):042124. doi: 10.1103/PhysRevE.95.042124. Epub 2017 Apr 14.
We investigate the statistics of heat exchange between a finite system coupled to reservoir(s). We have obtained analytical results for heat fluctuation theorems in the transient regime considering the Hamiltonian dynamics of the composite system consisting of the system of interest and the heat bath(s). The system of interest is driven by an external protocol. We first derive it in the context of a single heat bath. The result is in exact agreement with known result. We then generalize the treatment to two heat baths. We further extend the study to quantum systems and show that relations similar to the classical case hold in the quantum regime. For our study we invoke von Neumann two-point projective measurement in quantum mechanics in the transient regime. The study of quantum systems follows the same lines of argument as that of the classical system, and as a result the treatment used in the latter complements that used in the former. Our result is a generalization of Jarzynski-Wòjcik heat fluctuation theorem.
我们研究了与一个或多个热库耦合的有限系统之间的热交换统计。考虑到由感兴趣的系统和热库组成的复合系统的哈密顿动力学，我们已经获得了瞬态热涨落定理的解析结果。感兴趣的系统由外部协议驱动。我们首先在单个热库的背景下推导它。结果与已知结果完全一致。然后我们将处理方法推广到两个热库。我们进一步将研究扩展到量子系统，并表明在量子区域中存在与经典情况类似的关系。在我们的研究中，我们在瞬态区域调用量子力学中的冯·诺依曼两点投影测量。量子系统的研究遵循与经典系统相同的论证思路，因此后者使用的处理方法补充了前者使用的方法。我们的结果是雅尔津斯基 - 沃伊奇克热涨落定理的推广。
