论文标题
tsallis $ q = 3 $熵在紧凑的相位空间上描述的信息移动动力学
Information Shift Dynamics Described by Tsallis $q=3$ Entropy on a Compact Phase Space
论文作者
论文摘要
最近的数学研究表明，在非常一般的条件下，指数混合意味着Bernoulli特性。作为一种统计力学的具体示例，该统计力学是指数级混合的，我们考虑了由任意订单的Chebyshev Maps $ n \ geq 2 $的Bernoulli Shift Dynamics，它最大化Tsallis $ q = 3 $ entropy，而不是普通的$ Q = 1 $ Q = 1 $ boltzmann-gibbs Entropy。在创建普通时空之前，这种信息转移动态可能与预上有关。我们讨论了耦合的Chebyshev系统的对称属性，该系统的均匀和奇数$ n $不同。我们表明，在这种情况下，罚款结构常数$α_{el} = 1/137 $的值将其区分为耦合常数，从而导致在相应的耦合地图晶格的空间方向上无关的行为，$ n = 3 $。
Recent mathematical investigations have shown that under very general conditions exponential mixing implies the Bernoulli property. As a concrete example of a statistical mechanics which is exponentially mixing we consider a Bernoulli shift dynamics by Chebyshev maps of arbitrary order $N\geq 2$, which maximizes Tsallis $q=3$ entropy rather than the ordinary $q=1$ Boltzmann-Gibbs entropy. Such an information shift dynamics may be relevant in a pre-universe before ordinary space-time is created. We discuss symmetry properties of the coupled Chebyshev systems, which are different for even and odd $N$. We show that the value of the fine structure constant $α_{el}=1/137$ is distinguished as a coupling constant in this context, leading to uncorrelated behaviour in the spatial direction of the corresponding coupled map lattice for $N=3$.
