Institute of Theoretical Science and Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, USA.
Phys Rev E. 2019 Oct;100(4-1):042105. doi: 10.1103/PhysRevE.100.042105.
We construct a finite bath with variable temperature for quantum thermodynamic simulations in which heat flows between a system S and the bath environment E in time evolution of an initial SE pure state. The bath consists of harmonic oscillators that are not necessarily identical. Baths of various numbers of oscillators are considered; a bath with five oscillators is used in the simulations. The bath has a temperaturelike level distribution. This leads to definition of a system-environment microcanonical temperature T_{SE}(t) which varies with time. The quantum state evolves toward an equilibrium state which is thermal-like, but there is significant deviation from the ordinary energy-temperature relation that holds for an infinite quantum bath, e.g., an infinite system of identical oscillators. There are also deviations from the Einstein quantum heat capacity. The temperature of the finite bath is systematically greater for a given energy than the infinite bath temperature, and asymptotically approaches the latter as the number of oscillators increases. It is suggested that realizations of these finite-size effects may be attained in computational and experimental dynamics of small molecules.
我们构建了一个具有变温的有限浴，用于量子热力学模拟，其中在初始 SE 纯态的时间演化中，系统 S 和浴环境 E 之间发生热流。浴由非完全相同的谐振子组成。考虑了各种数量的谐振子浴，在模拟中使用了五个谐振子浴。浴具有类似于温度的能级分布。这导致定义了随时间变化的系统-环境微正则温度 T_{SE}(t)。量子态朝着类似于热的平衡态演化，但与普通的能量-温度关系存在显著偏差，例如，对于无限量子浴，即相同谐振子的无限系统。也存在与爱因斯坦量子热容的偏差。对于给定能量，有限浴的温度比无限浴温度系统地更高，并且随着谐振子数量的增加，它渐近地接近后者。有人建议，在小分子的计算和实验动力学中可能会实现这些有限尺寸效应。
