Gauge Freedom of Entropies on q-Gaussian Measures
Gauge Freedom of Entropies on q-Gaussian Measures
复制标题
用 q-高斯测度衡量熵的自由度
DOI：
10.1007/978-3-030-65459-7_6
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Takatsu Asuka
中科院分区：
文献类型：
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作者：
Matsuzoe Hiroshi;Takatsu Asuka
Aq-高斯测度是高斯测度的推广。这种推广是通过用指数（）的幂函数代替指数函数来获得的。极限情况恢复高斯测度。在真实的线上的全q-高斯密度集上，护送期望决定了信息的几何结构，如熵和相对熵。随机变量的一般期望是随机变量关于其规律的积分。护送期望允许我们用任何其他措施取代法律。全q-高斯密度集合上最重要的护送期望之一是q-护送期望，因为该护送期望决定了Tsallis熵和Tsallis相对熵。熵的自由度现象是不同的护送期望决定相同的熵，但相对熵不同。在这一章中，我们首先介绍了q-对数函数的一个加细。然后我们利用加细的q-对数函数证明了在真实的直线上全q-高斯密度开集上的这一现象。我们写下相应的黎曼度量。
Aq-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent(). The limit caserecovers a Gaussian measure. On the set of allq-Gaussian densities over the real line with, escort expectations determine information geometric structures such as an entropy and a relative entropy. The ordinary expectation of a random variable is the integral of the random variable with respect to its law. Escort expectations admit us to replace the law by any other measures. One of the most important escort expectations on the set of allq-Gaussian densities is theq-escort expectation since this escort expectation determines the Tsallis entropy and the Tsallis relative entropy. The phenomenongauge freedom of entropiesis that different escort expectations determine the same entropy, but different relative entropies. In this chapter, we first introduce a refinement of theq-logarithmic function. Then we demonstrate the phenomenon on an open set of allq-Gaussian densities over the real line by using the refinedq-logarithmic functions. We write down the corresponding Riemannian metric.