发表机构
The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示熵产生信息几何的内在各向异性，通过量子相对熵的层级投影得到精确正交分解，并导出各分量不同的几何界限，结合动力学速度极限获得基于物理可观测量的严格熵产生界限。
AI 中文摘要
我们揭示熵产生的信息几何表现出内在的各向异性，为其不同分量所遵循的不等价几何约束提供了统一起源。利用量子相对熵的层级投影结构，我们推导出熵产生的一个精确正交分解，将其分为三个不同的几何贡献，分别与吉布斯投影温度偏离参考温度、环境偏离其吉布斯投影态以及系统-环境关联相关。我们证明这些贡献遵循根本不同的几何界限：第一个贡献简化为经典Kullback-Leibler散度，且仅依据迹距离及系统和环境维度不存在通用上界；而后两个贡献则承认具有维度相关因子的严格基于距离的界限。该框架同样适用于仅以系统状态描述的经典马尔可夫动力学，在此情形下分解中不存在系统-环境关联贡献。将此几何分解与动力学速度极限相结合，我们获得了仅以物理可访问量（如平均能量和哈密顿量方差）表示的熵产生的严格界限。
英文摘要
We reveal that the information geometry of entropy production exhibits an intrinsic anisotropy, providing a unified origin for the inequivalent geometric constraints obeyed by its different components. Using a hierarchical projection structure of quantum relative entropy, we derive an exact orthogonal decomposition of entropy production into three distinct geometric contributions associated with the deviation of the Gibbs projection temperature from the reference temperature, the deviation of the environment from its Gibbs projection state, and system--environment correlations. We demonstrate that these contributions obey fundamentally different geometric bounds: the first reduces to a classical Kullback--Leibler divergence and admits no universal upper bound in terms of the trace distance and the system and environment dimensions alone, whereas the latter two admit rigorous distance-based bounds with dimension-dependent factors. The framework also applies to classical Markovian dynamics described solely in terms of the system state, for which the system--environment correlation contribution is absent from the decomposition. Combining this geometric decomposition with dynamical speed limits, we obtain rigorous bounds on entropy production expressed solely in terms of physically accessible quantities, such as the mean energy and Hamiltonian variance.
Comments11 pages, 3 figures
