发表机构
School of Basic Sciences, Indian Institute of Technology Bhubaneswar（印度理工学院布巴内斯瓦尔基础科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建具有相同可见统计但不同隐藏动力学关联的马尔可夫模型，证明熵条件历史可呈现不同集体相，并揭示第四累积量在临界与无序系统中的关键作用。
AI 中文摘要
可见动力学和平均耗散不一定决定稀有历史的集体相。我们构建了具有相同普通可见路径分布、稳态、平均熵产生、平均跳跃活性和驱动亲和力的局部马尔可夫模型，然而当历史按其完整熵产生加权时，这些模型却呈现不同的相。可见构型调制隐藏的驱动循环，其精确消除将动力学关联转化为相互作用。正谱约化将隐藏弛豫与集体模式分离。周期二元模型在熵方差于每个观测时间匹配的情况下仍保持相反的相。对于守恒粒子，一对模型在熵和隐藏活性的前两个联合累积量于每个观测时间均匹配，却分别选择分离态或具有抑制长波长密度噪声的涨落态。束缚态输运和费米子演化决定了它们截然不同的动力学。在干净的伊辛临界中点，熵源与热扰动二次耦合，使得第四累积量成为第一个检测临界磁化率的量。其每格点速率对数增长，精确截断由系统尺寸和观测时间设定。对于两种淬火无序系综，精确样本响应公式和数值证据支持有限的第四累积量密度，尽管弛豫非常缓慢；弱无序连续体响应允许受控的博雷尔求和。一个共同的正隐藏特征向量表征自主选择的动力学。当此条件不成立时，有限网络在保持其普通可见过程和平均诊断的同时发展出可见记忆。这些结果识别了聚合热力学观测所遗漏的动力学信息。
英文摘要
Visible dynamics and mean dissipation need not determine the collective phases of rare histories. We construct local Markov models with identical ordinary visible path distributions, stationary states, mean entropy production, mean jump activity and driving affinities, yet different phases when histories are weighted by their full entropy production. Visible configurations modulate hidden driven cycles, whose exact elimination turns kinetic correlations into interactions. A positive spectral reduction separates hidden relaxation from collective modes. Periodic binary models retain opposite phases with entropy variances matched at every observation time. For conserved particles, a pair matches the first two joint cumulants of entropy and hidden activity at every observation time, yet selects segregation or a fluctuating state with suppressed long-wavelength density noise. Bound-state transport and fermionic evolution determine their contrasting dynamics. At a clean Ising critical midpoint, the entropy source couples quadratically to the thermal perturbation, making the fourth cumulant the first to detect the critical susceptibility. Its rate per site grows logarithmically, with an exact cutoff set by system size and observation time. For two quenched disorder ensembles, exact sample-response formulas and numerical evidence support a finite fourth-cumulant density despite very slow relaxation; a weak-disorder continuum response admits a controlled Borel sum. A common positive hidden eigenvector characterizes autonomous selected dynamics. When this condition fails, a finite network develops visible memory while preserving its ordinary visible process and mean diagnostics. These results identify kinetic information missed by aggregate thermodynamic observations.
Comments35 pages including appendices, 7 figures, 1 table
