Anza Fabio, Crutchfield James P
Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.
Phys Rev E. 2022 Nov;106(5-1):054102. doi: 10.1103/PhysRevE.106.054102.
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We focus on microcanonical and canonical ensembles, looking at the geometric counterpart of Gibbs ensembles for distributions on the space of quantum states. We show that one can define quantum heat and work in an intrinsic way, including single-trajectory work. We reformulate thermodynamic entropy in a way that accords with classical, quantum, and information-theoretic entropies. We give both the first and second laws of thermodynamics and Jarzynki's fluctuation theorem. Overall, this results in a more transparent physics than conventionally available. The mathematical structure and physical intuitions underlying classical and quantum dynamics are seen to be closely aligned. The experimental relevance is brought out via a stochastic model for chiral molecules (in the two-state approximation) and Josephson junctions. Numerically, we demonstrate this invariably leads to the emergence of the geometric canonical ensemble.
基于几何量子力学与经典力学之间的相似性，我们探索了一种量子热力学的替代基础，该基础利用了基础态空间的微分几何。我们专注于微正则系综和正则系综，研究量子态空间上分布的吉布斯系综的几何对应物。我们表明，可以以一种内在的方式定义量子热和功，包括单轨迹功。我们以一种与经典熵、量子熵和信息论熵相一致的方式重新表述热力学熵。我们给出了热力学第一定律和第二定律以及雅津斯基涨落定理。总体而言，这导致了比传统方法更清晰的物理学。经典动力学和量子动力学背后的数学结构和物理直觉被认为紧密相关。通过手性分子的随机模型（在二态近似下）和约瑟夫森结展示了其实验相关性。在数值上，我们证明这总是会导致几何正则系综的出现。
