论文标题
椭圆形，可集成系统和玻尔兹曼定理的定理
A Theorem on Ellipses, an Integrable System and a Theorem of Boltzmann
论文作者
论文摘要
我们研究了鲍尔茨曼（Boltzmann）在1868年考虑的机械系统，该机械系统是在规范和微型典型集合的推导下进行的。引入了该系统作为Ergodic Dynamics的一个例子，这对于Boltzmann的推导至关重要。它由二维中的一个粒子组成，该粒子受到固定中心的重力吸引力。另外，无限平面固定在距中心的某个有限距离上，该距离是粒子在弹性上碰撞的硬壁。最后，添加了额外的离心力。我们将表明，在没有这种额外的离心力的情况下，有两个独立的运动积分。因此，额外的离心力对于鲍尔茨曼（Boltzmann）主张持有的主张是必要的。
We study a mechanical system that was considered by Boltzmann in 1868 in the context of the derivation of the canonical and microcanonical ensembles. This system was introduced as an example of ergodic dynamics, which was central to Boltzmann's derivation. It consists of a single particle in two dimensions, which is subjected to a gravitational attraction to a fixed center. In addition, an infinite plane is fixed at some finite distance from the center, which acts as a hard wall on which the particle collides elastically. Finally, an extra centrifugal force is added. We will show that, in the absence of this extra centrifugal force, there are two independent integrals of motion. Therefore the extra centrifugal force is necessary for Boltzmann's claim of ergodicity to hold.
