论文标题
KAC进化的信息衰减
Decay of Information for the Kac Evolution
论文作者
论文摘要
我们考虑与$ n \ gg m $颗粒的热储存液接触的$ m $颗粒系统。系统和储层的演变以及它们的相互作用是通过KAC的主方程建模的。我们选择了总能量$ n+m $的初始分布，并表明，如果储层最初处于平衡状态，即如果初始分布仅取决于储层中粒子的能量，则系统的熵将系统的熵呈指数衰减至非常小的值。我们将证明基于类似属性以获取信息。类似的论点使我们能够大大简化[2]中主要结果的证明。
We consider a system of $M$ particles in contact with a heat reservoir of $N\gg M$ particles. The evolution in the system and the reservoir, together with their interaction, are modeled via the Kac's Master Equation. We chose the initial distribution with total energy $N+M$ and show that if the reservoir is initially in equilibrium, that is if the initial distribution depends only on the energy of the particle in the reservoir, then the entropy of the system decay exponentially to a very small value. We base our proof on a similar property for the Information. A similar argument allows us to greatly simplify the proof of the main result in [2].
