论文标题
最佳运输的热力学统一：热力学不确定性关系，最小耗散和热力学速度极限
Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
论文作者
论文摘要
热力学是从能量角度研究物理系统的通用手段。近年来，随机和量子热力学领域的建立，热力学的思想已被推广到小波动系统。最佳运输理论在数学和统计中独立开发，涉及可以将源分布最佳运输到目标分布的手段，从而在概率分布之间得出了有用的指标，称为Wasserstein距离。尽管它们看似无关，但这些领域之间的紧密联系在连续状态Langevin Dynamics的背景下已经揭幕，这对非平衡系统产生了一些重要含义。在这项研究中，我们通过开发一个用于离散最佳运输的热力学框架来阐明离散病例的类似连接。我们首先引入了一种称为动力学状态迁移率的新型数量，该数量可显着改善热力学不确定性关系，并提供有关非平衡马尔可夫跳跃过程中电流精度的见解。然后，我们得出了将离散的瓦斯汀距离连接到主方程所描述的离散的马尔可维亚动力学的随机和量子热力学的变异公式。具体而言，我们严格地证明，瓦斯汀距离等于所有可接受的马尔可夫动力学对不可逆的熵产生和动态状态迁移率的最小产物。这些公式不仅统一了热力学和最佳转运理论之间的关系，而且还将其推广到量子情况。此外，我们证明获得的变异公式导致了随机和量子热力学中的显着应用。
Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics.
