不同温度下热库动力学模型稳态的探讨
Approach to the steady state in kinetic models with thermal reservoirs at different temperatures
摘要：
我们继续调查的动力学模型的系统接触，通过随机相互作用与几个空间均匀的热储在不同的温度。考虑到模型不同于以前的工作中所研究的，我们明确计算的唯一空间均匀的非平衡稳态（NESS），并证明它是指数快速接近从任何均匀的初始状态。这就留下了一个问题，即是否存在空间不均匀的NESS。进一步简化我们的模型，然后我们证明了不存在这样的NESS和指数的方法，唯一的空间均匀的NESS（与可计算的有界率）。证明的方法依赖于精细Doeblin估计和其他probabilisitic技术，是完全不同的分析，在早期的工作是基于压缩映射方法。
英文摘要：
We continue the investigation of kinetic models of a system in contact via stochastic interactions with several spatially homogeneous thermal reservoirs at different temperatures. Considering models different from those investigated in earlier work, we explicitly compute the unique spatially uniform non-equilibrium steady state (NESS) and prove that it is approached exponentially fast from any uniform initial state. This leaves open the question of whether there exist NESS that are not spatially uniform. Making a further simplification of our models, we then prove non-existence of such NESS and exponential approach to the unique spatially uniform NESS (with a computably boundable rate). The method of proof relies on refined Doeblin estimates and other probabilisitic techniques, and is quite different form the analysis in earlier work that was based on contraction mapping methods.
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