THERMODYNAMIC FORMALISM FOR AMENABLE GROUPS AND COUNTABLE STATE SPACES

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-15 DOI:10.1017/s1474748024000112

Elmer R. Beltrán, Rodrigo Bissacot, Luísa Borsato, Raimundo Briceño

引用次数: 0

Abstract

Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties, such as an infimum rule. Next, we extend the definitions of different notions of Gibbs measures and prove their existence and equivalence, given some regularity and normalization criteria on the potential. Finally, we provide a family of potentials that nontrivially satisfy the conditions for having this equivalence and a nonempty range of inverse temperatures where uniqueness holds.

查看原文本刊更多论文

可合并群和可数状态空间的热力学形式主义

考虑到在可数组上的可数状态空间上的全转移，我们发展了它的热力学形式主义。首先，我们引入了压力的概念，并利用平铺技术证明了它的存在性和进一步的性质，如最小值规则。接下来，我们扩展了吉布斯量度不同概念的定义，并证明了它们的存在性和等价性，同时给出了势的一些规则性和归一化标准。最后，我们提供了一个势族，它非绝对地满足了具有这种等价性的条件，并提供了一个反温度的非空范围，其中唯一性成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.