发表机构
Weizmann Institute of Science; University of Freiburg; Max Planck Institute for Multidisciplinary Sciences（魏茨曼科学研究所; 弗赖堡大学; 马克斯·普朗克多学科科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过正则变换将多热库系统映射为受哈密顿旋度力驱动的单热库系统，揭示非平衡电流的力学起源，并给出精确解与平衡化方案。
AI 中文摘要
我们研究了一个与多个不同温度热库耦合的系统的统计力学，这种设置通常维持非平凡的循环。通过应用正则变换，我们将系统映射为单个粒子与单一热库耦合但受确定性旋度力（一种可逆的、与速度无关的、具有非零旋度的非保守力）驱动的系统，该系统可以用具有各向异性动能项的哈密顿量描述。尽管具有哈密顿结构，系统并不弛豫到相应的玻尔兹曼分布，而是真正处于非平衡态。该映射为多温度系统中的电流提供了力学解释，我们通过两个例子加以说明。特别是，循环方向可以从确定性力场中定性预测。对于精确可解的$N$维欠阻尼Ornstein-Uhlenbeck过程，我们推导了稳态分布和熵产生率的显式表达式，强调了力场的（广义）旋度在驱动系统偏离热平衡中的作用。最后，我们展示了如何使用非保守力精确地使任何与多个热库耦合的系统达到平衡，并获得相应的平衡分布。
英文摘要
We investigate the statistical mechanics of a system coupled to multiple heat reservoirs at different temperatures, a setting which typically sustains nontrivial circulation. By applying a canonical transformation, we map the system onto that of a particle coupled to a single reservoir yet driven by a deterministic curl-force---a reversible, velocity-independent non-conservative force with non-vanishing curl---that can be described by a Hamiltonian with an anisotropic kinetic energy term. Despite the Hamiltonian structure, the system does not relax to the corresponding Boltzmann distribution, and is genuinely out of equilibrium. The mapping provides a mechanical interpretation of the currents in multi-temperature systems, as we demonstrate by means of two examples. In particular, the direction of circulation is qualitatively predictable from the deterministic force field. For the exactly solvable case of an $N$-dimensional underdamped Ornstein-Uhlenbeck process, we derive explicit expressions for the steady-state distribution and the entropy production rate, highlighting the role of the (generalized) curl of the force field in driving the system out of thermal equilibrium. Finally, we show how a non-conservative force can be used to exactly equilibrate any system coupled to multiple reservoirs, and obtain the corresponding equilibrium distribution.
Comments14 pages, 2 figures, SI appendix: SI_arxiv.tex
