论文标题
信息几何形状和弗罗贝尼乌斯代数
Information geometry and Frobenius algebra
论文作者
论文摘要
我们表明，frobenius stercrcture等同于信息几何形状中的双重平坦坚固。我们在统计歧管的切线空间上定义了一个乘积结构，我们称之为统计产品。我们还定义了标量数量，我们称之为Yukawa术语。通过显示统计力学中的两个示例，首先是经典的理想气体，其次是量子玻色子理想气体，我们认为Yukawa术语量化了信息生成，这类似于通过两个费米子和Higgs玻色子的3点相互作用产生质量的方式。在经典情况下，Yukawa项的术语相同零，而在量子情况下，随着逃逸的量为零，Yukawa项差异为零，这表明Bose-Einstein凝结。
We show that a Frobenius sturcture is equivalent to a dually flat sturcture in information geometry. We define a multiplication structure on the tangent spaces of statistical manifolds, which we call the statistical product. We also define a scalar quantity, which we call the Yukawa term. By showing two examples from statistical mechanics, first the classical ideal gas, second the quantum bosonic ideal gas, we argue that the Yukawa term quantifies information generation, which resembles how mass is generated via the 3-points interaction of two fermions and a Higgs boson (Higgs mechanism). In the classical case, The Yukawa term is identically zero, whereas in the quantum case, the Yukawa term diverges as the fugacity goes to zero, which indicates the Bose-Einstein condensation.
