We consider Kac’s 1D N-particle system coupled to an ideal thermostat at a fixed temperature, introduced by Bonetto, Loss, and Vaidyanathan in 2014. We obtain a propagation of chaos result for this system, with an explicit and uniform-in-time rate of order \(N^{-1/3}\) in terms of the 2-Wasserstein metric squared. We also show well-posedness and equilibration for the limit kinetic equation in the space of probability measures. The proofs use a coupling argument previously introduced by Cortez and Fontbona in 2016.

中文翻译：

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恒温Kac模型的混沌均匀传播

我们考虑了由Bonetto，Loss和Vaidyanathan于2014年引入的Kac的一维N粒子系统与固定温度下理想恒温器的耦合。我们获得了该系统的混沌结果传播，具有明确且及时的速率的顺序\（N ^ { - 1/3} \）在2瓦瑟斯坦度量平方的条款。我们还展示了概率度量空间中极限动力学方程的适定性和平衡性。证明使用的是先前由Cortez和Fontbona在2016年引入的耦合参数。