论文标题
在恒定能的表面上的相空间中的随机运动
Stochastic motion in phase space on a surface of constant energy
论文作者
论文摘要
我们研究了除了保守力之外，还受到随机力的封闭系统。随机方程的设置是以使能量始终严格保守的方式。为了确保这种保护定律，使用不是ITô或Stratonovic解释的随机运动方程的适当解释来得出概率密度的演化方程。相空间中的轨迹仅限于恒定能的表面。尽管有这种限制，但熵被证明会随着时间而增加，表达了不可逆转的行为和平衡的放松。当前方法的主要结果与liouville方程式所给出的方法形成鲜明对比，该方程式也描述了封闭的系统，但并未显示不可逆性。
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure this conservation law, the evolution equation for the probability density is derived using an appropriate interpretation of the stochastic equation of motion that is not the Itô nor the Stratonovic interpretation. The trajectories in phase space are restricted to the surface of constant energy. Despite this restriction, the entropy is shown to increase with time, expressing irreversible behavior and relaxation to equilibrium. This main result of the present approach contrasts with that given by the Liouville equation, which also describes closed systems, but does not show irreversibility.
