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.

中文翻译：

---

适用于可调节群和可数状态空间的热力学形式主义

考虑到可数服从群上可数状态空间的完全转变，我们开发了它的热力学形式主义。首先，我们引入压力的概念，并使用平铺技术证明其存在和进一步的属性，例如下确界规则。接下来，我们扩展吉布斯测度不同概念的定义，并在给定势的一些规律性和标准化标准的情况下证明它们的存在性和等价性。最后，我们提供了一系列势能，这些势能非常满足具有这种等价性的条件以及唯一性成立的非空逆温度范围。