对于可微分动态系统的经典费舍尔信息
Mohamed Sahbani1,2, Swetamber Das1,2, Jason R Green1,2
1Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.
Chaos (Woodbury, N.Y.)
|October 27, 2023
概括
我们为确定性系统引入了一个新的经典信息度量,从混乱动态中的初始条件灵敏度量化不确定性. 这个测量与相位空间曲率和流速有关.
科学领域:
- 经典机械学 经典机械学
- 信息理论是信息理论.
- 动态系统理论 动态系统理论
背景情况:
- 费舍尔信息为经典和量子系统的参数估计提供了一个下限的不确定性.
- 确定性动态系统,即使没有噪声,也表现出不确定性,原因是初始条件扰动的指数增长,这是混乱的标志.
研究的目的:
- 引入一种新的古典信息测量方法,用于孤立,封闭或开放系统中的确定性动态.
- 开发一种不同于经典的费舍尔信息的不确定性度量,类似于量子费舍尔信息.
主要方法:
- 定义使用触点空间中的利亚普诺夫向量来测量新的经典信息.
- 分析局部状态空间结构和线性稳定性,以推导信息测量的边界.
- 在说明性机械系统上执行数值计算.
主要成果:
- 新的信息测量量量化了确定性混乱系统中的不确定性.
- 它是使用Lyapunov向量定义的,类似于量子费舍尔信息如何使用波向量.
- 导出的上下边界将测量量解释为流的净拉伸作用.
- 数值结果显示了相位空间曲率和流速的依赖性.
结论:
- 拟议的经典信息措施为确定性动态中的不确定性提供了新的视角.
- 这种测量提供了关于相位空间内的拉伸动态的见解.
- 这些发现将信息理论概念与混乱机械系统的研究联系起来.
相关概念视频
01:31Classification of Systems-II
150
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
150
01:21Linear Approximation in Time Domain
85
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
85
01:26Linear Approximation in Frequency Domain
94
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
94
01:26Classification of Systems-I
191
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
191
01:18Second Order systems II
115
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
115
01:21First Order Systems
97
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
97