Entropy and maximal entropy in Markov systems

马尔可夫系统中的熵和最大熵

• 批准号: LX0346775
• 负责人: Prof Anthony Dooley
• 金额: $ 0.41万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Linkage - International
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/LX0346775
• 关键词: Entropy; maximal; entropy; Markov; systems

Entropy is a measure of how well-ordered a system is: chaotic systems have high entropy. Two approaches to entropy are available, via the limiting behaviour of the orbits of points, which yields topological entropy, and via the behaviour of the distributions of measures of partitions, yielding measure-theoretic entropy. The topological entropy is the least upper bound of entropies of all possible measures. We study when there is a measure which realises this bound, describing the structure of such systems via Markov and Bratteli diagrams. Our methods will be applied to new versions of entropy for non-singular systems. This will assist in the description of chaotic behaviour.

熵是对系统有序程度的衡量：混沌系统具有高熵。熵的两种方法是可用的，通过点轨道的极限行为，它产生拓扑熵，以及通过分区的度量分布的行为，产生测量理论熵。拓扑熵是所有可能测度的熵的最小上界。我们研究了什么时候有一个测度实现了这一界限，并通过马尔可夫图和布拉特利图描述了这类系统的结构。我们的方法将应用于非奇异系统的熵的新版本。这将有助于混沌行为的描述。