标题： 热力学一致的粗粒化：通过第二量子化从相互作用粒子到场 显示英文标题

标题： Thermodynamically Consistent Coarse-graining: from Interacting Particles to Fields via Second Quantization

摘要： 我们系统地推导了相互作用粒子的精确粗粒化描述，其具有热力学一致的随机动力学，适用于不同观察尺度，即介观和宏观尺度。 我们使用Doi-Peliti场论实现粗粒化过程，该过程在介观/宏观尺度上保留微观噪声效应。 精确映射揭示了泊松粒子占据统计的关键作用。 我们通过一个典型的群体运动模型，即活性伊辛模型，展示了精确粗粒化方法的含义，该模型表现出微观和宏观平均场粗粒化描述之间的不匹配。 我们的分析表明，高密度和低密度区域分别由两种不同的粗粒化方程支配。 在低密度区域，噪声效应起着显著作用，导致一阶相变。 相反，在高密度区域发生二阶相变。 由于精确的粗粒化方法，我们的框架还拓展了在其他相互作用粒子模型中系统分析噪声诱导相变的应用性。 显示英文摘要

摘要： We systematically derive an exact coarse-grained description for interacting particles with thermodynamically consistent stochastic dynamics, applicable across different observation scales, the mesoscopic and the macroscopic. We implement the coarse-graining procedure using the Doi-Peliti field theory, which preserves microscopic noise effects on the meso/macro scale. The exact mapping reveals the key role played by Poissonian particle occupancy statistics. We show the implications of the exact coarse-graining method using a prototypical flocking model, namely the active Ising model, which exhibits a mismatch between the microscopic and macroscopic mean-field coarse-grained descriptions. Our analysis shows that the high- and low-density regimes are governed by two different coarse-grained equations. In the low-density regime, noise effects play a prominent role, leading to a first-order phase transition. In contrast, the second-order phase transition occurs in the high-density regime. Due to the exact coarse-graining methods, our framework also opens up applicability to systematically analyze noise-induced phase transitions in other models of reciprocally and non-reciprocally interacting particles.