论文标题
在复杂过程中，信息生产和广义熵的等效性
Equivalence of information production and generalized entropies in complex processes
论文作者
论文摘要
以强相关性和脂肪尾分布功能为特征的复杂系统被认为在Boltzmann-Gibbs熵的框架内是不兼容的。作为替代方案，提出并深入研究了所谓的广义熵。在这里，我们表明这种不兼容是一种误解。对于广泛的过程，Boltzmann熵该对数多样性仍然是有效的熵概念，但是，对于非I.I.D。，非媒体词和非共生过程，Boltzmann熵不是Shannon形式。玻尔兹曼熵的正确形式可以证明与广义熵相同。我们为所有过程得出此结果，这些过程可以可逆地映射到过程为I.I.D ..中的伴随表示。在这些表示中，信息生产由香农熵给出。我们证明，在原始采样空间上，这会产生与广义熵相同的功能。因此，构建适当上下文敏感熵功能的问题可以转化为查找伴随表示的更简单的问题。该方法为密切相关的系统和复杂过程的统计物理学提供了一个综合框架。
Complex systems that are characterized by strong correlations and fat-tailed distribution functions have been argued to be incompatible within the framework of Boltzmann-Gibbs entropy. As an alternative, so-called generalized entropies were proposed and intensively studied. Here we show that this incompatibility is a misconception. For a broad class of processes, Boltzmann entropy the log multiplicity remains the valid entropy concept, however, for non-i.i.d., non-multinomial, and non-ergodic processes, Boltzmann entropy is not of Shannon form. The correct form of Boltzmann entropy can be shown to be identical with generalized entropies. We derive this result for all processes that can be mapped reversibly to adjoint representations where processes are i.i.d.. In these representations the information production is given by the Shannon entropy. We proof that over the original sampling space this yields functionals that are identical to generalized entropies. The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes.
