AI 中文总结
本文研究两珠耦合非平衡稳态模型，用协方差矩阵与朗之万动力学模拟，揭示动力学温度的核心作用，推导有效温度，发现时间平均可观测量收敛更快。
AI 中文摘要
我们研究了一个非平衡稳态模型，该模型由两个任意质量的耦合珠构成，分别与两个不同温度的热库接触。通过协方差矩阵方法结合欠阻尼朗之万动力学的数值模拟，我们表征了稳态概率分布、热输运和熵产生。结果表明，熵产生和热流等不可逆性度量在珠质量交换下保持不变，而能量存储可观测量在对称结构中明确依赖于质量排布。这揭示了一个根本区别：能量可观测量在奇异质量极限下表现出路径依赖性，而输运和不可逆性仍有良好定义。我们还表明，动力学温度是支配系统热力学的自然变量：其差值控制输运和熵产生，其和通过模型特定的广义均分关系决定平均能量。在无限质量极限下，仅用动力学温度表示的本构关系仍有意义。因此，能量、输运和不可逆性通过动力学温度作为组织变量实现统一。我们还推导了一个有效温度，定义了类平衡的正则分布。最后，我们分析了遍历性概念，发现时间平均可观测量的收敛速度显著快于系综平均。
英文摘要
We investigate a nonequilibrium steady-state model consisting of two coupled beads with arbitrary masses in contact with two thermal baths at different temperatures. Using a covariance-matrix approach together with numerical simulations of the underdamped Langevin dynamics, we characterize steady-state probability distributions, heat transport, and entropy production. We show that irreversibility measures such as entropy production and heat current are invariant under an exchange of the bead masses, whereas energy-storage observables depend explicitly on the mass arrangement in a symmetrical set up. This reveals a fundamental distinction: energy observables exhibit path dependence in singular mass limits, while transport and irreversibility remain well defined. We show that kinetic temperatures provide the natural variables governing the thermodynamics of the system: their difference controls transport and entropy production, while their sum determines the mean energy via a model specific generalized equipartition relation. In the infinite-mass limit, only constitutive relations expressed in terms of kinetic temperatures remain meaningful. Thus, energy, transport, and irreversibility are unified through kinetic temperatures as the organizing variables. We also derive an effective temperature that defines an equilibrium-like canonical distribution. Finally, we analyze the notion of ergodicity and show that the time-averaged observables converge significantly faster than the ensemble averages.
Comments13 pages, 9 figures, 1 table
Journal refPhys. Rev. E 114, 034142 (2026)
