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

TL;DR

This paper develops an exact, thermodynamically consistent coarse-graining method for interacting particles using field theory, capturing noise effects and revealing different phase transition behaviors across density regimes.

Contribution

It introduces a novel coarse-graining framework via Doi-Peliti field theory that preserves microscopic noise effects and applies it to analyze phase transitions in active matter models.

Findings

Low-density regime exhibits first-order phase transition due to noise.

High-density regime shows second-order phase transition.

Framework applicable to various interacting particle systems.

Abstract

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.