Thermodynamically Consistent Coarse-graining: from Interacting Particles to Fields via Second Quantization
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| Format: | Preprint |
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2025
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| author | Mohite, Atul Tanaji Rieger, Heiko |
| author_facet | Mohite, Atul Tanaji Rieger, Heiko |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamically Consistent Coarse-graining: from Interacting Particles to Fields via Second Quantization Mohite, Atul Tanaji Rieger, Heiko Statistical Mechanics Soft Condensed Matter 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. |
| title | Thermodynamically Consistent Coarse-graining: from Interacting Particles to Fields via Second Quantization |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2508.11430 |