论文标题
从哈密顿系统的随机运动到玻尔兹曼·H定理和热力学的第二定律 - 路径概率的途径
From Random Motion of Hamiltonian Systems to Boltzmann H Theorem and Second Law of Thermodynamics -- a Pathway by Path Probability
论文作者
论文摘要
受保守力和高斯噪声的理想随机运动的数值实验表明，路径概率指数取决于动作。该分布意味着一个基本原理概括了哈密顿 - 拉格朗日力学的最小动作原理，并产生了随机动力学的力学形式。在该理论中，必须修改相密度分布保护的liouville定理，以允许相密度的时间演变，从而允许玻璃体定理。我们认为，在H定理的批评中未考虑常规的牛顿动力学与随机动态之间的差距。
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian-Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory, Liouville theorem of conservation of phase density distribution must be modified to allow time evolution of phase density and consequently the Boltzmann H theorem. We argue that the gap between the regular Newtonian dynamics and the random dynamics was not considered in the criticisms of the H theorem.
