论文标题
部分可观测时空混沌系统的无模型预测
Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
论文作者
论文摘要
在尺寸$ n $中任意力场$ \ vec f（\ vec r）$ n $中的非平衡fokker-planck动力学通过与标量潜在$ v（\ vec r）$和vector势能$ \ vec a（\ vec a（\ vec r）$ vec r）$ v（\ vec r）$ v（\ vec r）$ v（\ vec r）$ v（\ vec r）$ v的通讯来重新审视。不可逆性的相关参数是$ \ frac {n（n-1）} {2} $磁矩阵元素$ b_ {nm}（\ vec x）= -b_ {mn}（\ vec x）= \ vec x）= \ partial_n a_m（\ vec x）a_m（\ vec x） - \ vec x） - \ vect usement（\ vec x） - 矢量电位$ \ vec a（\ vec r）$的相应量规变换。这种量子解释更加富有成效，可以研究随机轨迹的所有时间添加可观察到的统计数据，因为它们的生成函数与其他标量和/或矢量电位相对应。我们的主要结论是，可以通过为每个目的选择适当的量规来大大简化其大偏差属性和相应的DOOB条件过程的构建。然后将该一般框架应用于尺寸$ n $中的Ornstein-uhlenbeck轨迹的特殊时间添加性观测值，它们的生成功能对应于涉及二次性标量势和线性矢量电势的量子传播器，即在恒定磁性矩阵中量子振动器。作为简单说明的例子，我们最终将重点放在尺寸$ n = 2 $的布朗陀螺仪上，以计算其随机轨迹的熵产生的较大偏差属性，并构建具有每单位时间熵产生的给定值的相应条件过程。
The non-equilibrium Fokker-Planck dynamics in an arbitrary force field $\vec f(\vec r)$ in dimension $N$ is revisited via the correspondence with the non-hermitian quantum mechanics in a scalar potential $V(\vec r)$ and a vector potential $\vec A(\vec r)$. The relevant parameters of irreversibility are then the $\frac{N(N-1)}{2}$ magnetic matrix elements $B_{nm}(\vec x ) =-B_{mn} (\vec x ) = \partial_n A_m (\vec x ) - \partial_m A_n (\vec x )$, while it is enlightening to explore the corresponding gauge transformations of the vector potential $\vec A(\vec r) $. This quantum interpretation is even more fruitful to study the statistics of all the time-additive observables of the stochastic trajectories, since their generating functions correspond to the same quantum problem with additional scalar and/or vector potentials. Our main conclusion is that the analysis of their large deviations properties and the construction of the corresponding Doob conditioned processes can be drastically simplified via the choice of an appropriate gauge for each purpose. This general framework is then applied to the special time-additive observables of Ornstein-Uhlenbeck trajectories in dimension $N$, whose generating functions correspond to quantum propagators involving quadratic scalar potentials and linear vector potentials, i.e. to quantum harmonic oscillators in constant magnetic matrices. As simple illustrative example, we finally focus on the Brownian gyrator in dimension $N=2$ in order to compute the large deviations properties of the entropy production of its stochastic trajectories and to construct the corresponding conditioned processes having a given value of the entropy production per unit time.
