We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle–Lanford functions, and the exposition is essentially self-contained.

中文翻译：

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移位空间上选择性解耦度量的大偏差和波动定理

我们建立了 Level-1 和 Level-3 大偏差原则 (LDPs)，用于在热力学形式不适用的非常一般的解耦条件下对有限字母表上的移位空间进行不变测量。这种解耦条件自然出现在多重分形分析、具有核心相互作用的吉布斯状态以及重复量子测量过程的统计中。我们还证明了 LDP 用于此类度量对的熵产生，并推导出相关的波动关系。证明基于 Ruelle-Lanford 函数，说明基本上是自包含的。