We study the thermodynamic formalism for particular types of sub-additive sequences on a class of subshifts over countable alphabets. The subshifts we consider include factors of irreducible countable Markov shifts under certain conditions, which we call irreducible countable sofic shifts. We show the variational principle for topological pressure for some sub-additive sequences with tempered variation on irreducible countable sofic shifts. We also study conditions for the existence and uniqueness of invariant ergodic Gibbs measures and the uniqueness of equilibrium states. Applications are given to some dimension problems and study of factors of (generalized) Gibbs measures on certain subshifts over countable alphabets.

中文翻译：

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隐藏吉布斯测量可数字母上的移位空间

我们研究了可数字母表上的一类子移位上特定类型的子加法序列的热力学形式。我们考虑的子位移包括在某些条件下不可约可数马尔可夫位移的因素，我们称之为不可约可数sofic位移。我们展示了一些子加性序列的拓扑压力的变分原理，这些序列在不可约可数sofic 位移上具有缓和变化。我们还研究了不变遍历吉布斯测度的存在和唯一性以及平衡状态的唯一性的条件。应用了一些维度问题和研究（广义）吉布斯测量对可数字母上的某些子移位的因素。