Hamilton形式与路径熵最大化
Hamiltonian formalism and path entropy maximization
摘要：
路径信息熵的最大化是在非平衡统计力学中构造模型的明确规定。在这里，它示出，根据这个处方的假设下，任意的瞬时约束的位置和速度，拉格朗日出现确定最可能的轨迹。根据非线性朗之万方程及其相关的福克-普朗克方程，偏离概率最大值可以用哈密顿量一致地描述为时间切片。路径熵最大化和朗之万/福克-普朗克方程之间的联系表明，相空间坐标的缺失信息永远不会随时间减少，这是热力学第二定律的纯信息理论版本。所有这些结果都与任何物理假设无关，因此对作为时间函数的任何广义坐标或任何其他参数都有效。这加强了第二定律是似然推理的基本性质的观点。
英文摘要：
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the Second Law of Thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the Second Law is a fundamental property of plausible inference.
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