论文标题
Gibbs统计歧管上的熵动态
Entropic dynamics on Gibbs statistical manifolds
论文作者
论文摘要
熵动力学是一个框架，在该框架中，动态定律被作为熵推理方法的应用。它的成功包括从概率原理中衍生量子力学和量子场理论。在这里，我们开发系统的熵动力学，其状态由概率分布描述。因此，动力学在统计歧管上展开，该统计歧管自动由信息几何形状提供的度量结构赋予。歧管的曲率具有重大影响。我们将动态重点放在Gibbs分布的统计歧管上（也称为规范分布或指数式家族）。该模型包括针对正在研究的系统量身定制的“熵”概念；该系统是其自己的时钟。正如人们可能期望的那样，熵时间本质上是方向性的。有一系列自然的箭头是熵考虑的。作为说明性示例，我们讨论了高斯和离散三州系统空间的动态。
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here we develop the entropic dynamics of a system the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold which is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an "entropic" notion of time that is tailored to the system under study; the system is its own clock. As one might expect, entropic time is intrinsically directional; there is a natural arrow of time which is lead by entropic considerations. As illustrative examples we discuss dynamics on a space of Gaussians and the discrete 3-state system.
