The Entropy of Square-Free Words

On the Entropy and Letter Frequencies of Ternary Square-Free Words

We enumerate all ternary length-l square-free words, which are words avoiding squares of words up to length l, for l<=24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary square-free words. We then consider ternary square-free words with fixed letter densities, thereby proving exponential growth for certain ensembles with various letter densities. We derive consequences for the free energy and entropy of ternary square-free words.

平方熵与一致 n-to-1 伯努利变换

Square Entropy and Uniform n-to-1 Bernoulli Transformations

本文定义了平方熵，证明了 n-to-1 全 zip shift 映射的内在遍历性，并揭示平方熵可刻画扩展伯努利变换类的 $(m,l)$-伯努利型一致 n-to-1 变换。

有限与无限实体守恒系统的广义熵方法：基于Havrda-Charvát-Tsallis熵的非高斯与非卡方分布对比基于Boltzmann-Shannon熵的高斯分布的见解

Generalized Entropy Approach for Conserved Systems with Finite vs Infinite Entities: Insights into Non-Gaussian and Non-Chi-Square Distributions using Havrda-Charvát-Tsallis Entropy vs Gaussian Distributions via Boltzmann-Shannon Entropy

本文用Havrda-Charvát-Tsallis熵推导有限实体守恒系统的最概然状态，得到非高斯与非卡方分布，并通过思想实验和计算机模拟验证，指出其在医学研究中的应用价值。