The Kac Model Coupled to a Thermostat
The Kac Model Coupled to a Thermostat
复制标题
与恒温器耦合的 Kac 模型
DOI：
10.1007/s10955-014-0999-6
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发表时间：
2013
影响因子：
1.6
通讯作者：
R. Vaidyanathan
中科院分区：
文献类型：
--
作者：
F. Bonetto;M. Loss;R. Vaidyanathan
本文研究了随机碰撞粒子与热浴相互作用的模型。粒子之间的碰撞是通过卡茨主方程建模，而恒温器被视为一个无限的气体在热平衡在反温度$$\beta $$β。该系统承认在逆温度下的正则分布$$\beta $$β作为唯一的平衡态。我们证明了任何初始分布的平衡分布指数快速的计算差距的发电机的发展，在一个适当的功能空间，以及通过证明相对熵指数衰减。我们还表明，演化传播混沌和一个粒子的边际，在大系统的限制，满足一个有效的玻尔兹曼型方程。
In this paper we study a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an infinite gas at thermal equilibrium at inverse temperature $$\beta $$β. The system admits the canonical distribution at inverse temperature $$\beta $$β as the unique equilibrium state. We prove that any initial distribution approaches the equilibrium distribution exponentially fast both by computing the gap of the generator of the evolution, in a proper function space, as well as by proving exponential decay in relative entropy. We also show that the evolution propagates chaos and that the one particle marginal, in the large system limit, satisfies an effective Boltzmann-type equation.