论文标题
关于牛顿运动方程与摩擦和随机噪声，Ostrogradsky-Inscomention和环境层次结构，Onsager-Machlup理论II的应用
On Newton's equation of motion with friction and stochastic noise, the Ostrogradsky-instability and the hierarchy of environments, An application of the Onsager-Machlup theory II
论文作者
论文摘要
Onsager和Machlup提出了一个二阶变量原则，以将惯性效应纳入langevin-equation中，从而使Lagrangian及时地具有二阶导数。这却违反了Ostrogradysky的定理，该定理证明，具有高于一阶衍生物的拉格朗日人毫无意义。结果，惯性效应不能以标准方式包括在内。通过使用规范形式主义，我们建议解决这个基本问题的解决方案。此外，我们提供了有关理想系统与几种环境之间沉浸和行动的层次结构的基本论点，并表明拉格朗日敏感的结构取决于该层次结构。
Onsager and Machlup proposed a second order variational-principle in order to include inertial effects into the Langevin-equation, giving a Lagrangian with second order derivatives in time. This but violates Ostrogradysky's theorem, which proves that Lagrangians with higher than first order derivatives are meaningless. As a consequence, inertial effects cannot be included in a standard way. By using the canonical formalism, we suggest a solution to this fundamental problem. Furthermore, we provide elementary arguments about the hierarchy of immersions and actions between an ideal system and several environments and show, that the structure of the Lagrangian sensitively depends on this hierarchy.
