Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar–Parisi–Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.

中文翻译：

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在排除过程中绘制当前和活动的波动图：后果和未解决的问题

考虑到不对称简单排除过程（ASEP）中活动和电流的较大偏差，我们表明两个参数不同的ASEP的活动和电流的联合尺度累积量生成函数之间存在不平凡的对应关系。通过对源模型的变形Markov矩阵应用相似度变换以获得目标模型的变形Markov矩阵，可以获取此映射。我们首先导出周期性边界条件的这种对应关系，并在扩散比例极限（对应于弱非对称简单排除过程，或WASEP）中显示映射如何用宏观波动理论（MFT）语言表达的。作为一个有趣的特定案例，我们将ASEP中电流的大偏差映射到SSEP中活动的大偏差，从而揭示SSEP中活动分布的Kardar–Parisi–Zhang体制。在高活性下，颗粒构型表现出高度均匀性[Jack等，PRL 114 060601（2015）]。利用量子自旋链理论的结果，我们通过评估半填充结构因子的小波数渐近行为来表征超均匀状态。相反，我们根据MFT结果得出一个推论，即在任何固定的总磁化强度（在热力学极限范围内）下自旋链中的相关函数。此外，我们将映射推广到具有边界储层的两个开放式ASEP的情况，并将其应用于MFT形式主义中的WASEP限制。