Motivated by various applications and examples, the standard notion of potential for dynamical systems has been generalized to almost additive and asymptotically additive potential sequences, and the corresponding thermodynamic formalism, dimension theory and large deviations theory have been extensively studied in the recent years. In this paper, we show that every such potential sequence is actually equivalent to a standard (additive) potential in the sense that there exists a continuous potential with the same topological pressure, equilibrium states, variational principle, weak Gibbs measures, level sets (and irregular set) for the Lyapunov exponent and large deviations properties. In this sense, our result shows that almost and asymptotically additive potential sequences do not extend the scope of the theory compared to standard potentials, and that many results in the literature about such sequences can be recovered as immediate consequences of their counterpart in the additive case. A corollary of our main result is that all quasi-Bernoulli measures are weak Gibbs.

中文翻译：

---

可加的、几乎可加的和渐近可加的势序列是等价的

在各种应用和例子的推动下，动力系统势的标准概念已被推广到几乎可加和渐近可加的势序列，并且相应的热力学形式主义、维数理论和大偏差理论近年来得到了广泛的研究。在本文中，我们证明了每一个这样的势序列实际上等价于一个标准（加性）势，因为存在一个具有相同拓扑压力、平衡状态、变分原理、弱吉布斯测度、水平集（和不规则集）用于 Lyapunov 指数和大偏差属性。从这个意义上说，我们的结果表明，与标准势相比，几乎和渐近可加的势序列并没有扩展理论的范围，并且文献中关于这些序列的许多结果可以作为它们在附加情况下的对应物的直接结果来恢复。我们主要结果的一个推论是所有准伯努利测度都是弱吉布斯测度。