论文标题
Lagrangian动力学在不均匀和热环境中，Onsager-Machlup理论I的应用
Lagrangian dynamics in inhomogeneous and thermal environments, An application of the Onsager-Machlup theory I
论文作者
论文摘要
我们直接从fokker-planck方程中直接得出了onsager-machlup lagrangian，并表明摩擦和耗散是运动方程的自然特性。我们开发了一种计算本地方差$σ_{2} \，b（q）^{2} $并将此功能识别为Helmholtz-factor的方法。在这两种含义中，函数$ b（q）$描述了环境的属性。对于应用，我们检查了通过气压介质的自由下落，并通过通过介质运行的孤子脉冲对风进行造型。我们处理沉浸在热浴中的谐波振荡器，发现直观和违反摩擦现象。通过允许温度与时间相关，冷却和加热的动态过程变得自愿可用。我们发现系统和环境之间的动态平衡状态。最后，我们表明动态平衡与绝热热力学过程有关。在特殊情况下，动态平衡可以诱导实际的相位转换。
We straight-forwardly derive the Onsager-Machlup Lagrangian from the Fokker-Planck equation and show that friction and dissipation are a natural property of the equation of motion. We develop a method to calculate the local variance $σ_{2}\,b(q)^{2}$ and identify this function as a Helmholtz-factor. In both meanings the function $b(q)$ describes properties of the environment. For application, we examine the free fall through a barometric medium and model a blow of wind by a solitonic pulse running through the medium. We treat harmonic oscillators immersed in a thermal bath, finding intuitive as well as counter-intuitive phenomena of friction. By allowing the temperature to be time-dependent, the dynamical process of cooling and heating becomes self-consistently available. We find a state of dynamical balance between system and environment. Last, we show that dynamical balance is related to adiabatic thermodynamic processes. In a special case, dynamical balance can induce a real phase-transition.
