Macroscopic fluctuation theory of interacting Brownian particles
arXiv:2512.15569 · doi:10.1103/1rvq-r3j1
Abstract
We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the collective diffusion coefficient, the MFT gives access to the exact large-scale dynamical properties of the system, both in- and out-of-equilibrium. In particular, we obtain exact results for dynamical correlations between the density and the current of particles. For one-dimensional systems, this allows us to obtain a precise description of these correlations for emblematic models, such as the Calogero and Riesz gases, and for systems with nearest-neighbor interactions such as the Rouse chain of hardcore particles or the recently introduced model of tethered particles. Tracer diffusion with the single-file constraint (but for arbitrary pairwise interaction) is also studied. For higher-dimensional systems, we quantitatively characterize these dynamical correlations by relying on standard methods such as the virial expansion.
23 pages, 15 figures
References in corpus (54)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Non equilibrium steady states: fluctuations and large deviations of the density and of the current
- Macroscopic fluctuation theory
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
- Langevin Equation for the Density of a System of Interacting Langevin Processes
- Current fluctuations in non-equilibrium diffusive systems: an additivity principle
- Macroscopic current fluctuations in stochastic lattice gases
- Distribution of current in non-equilibrium diffusive systems and phase transitions
- Physics and Mathematics of Calogero particles
- Single-File Diffusion of Atomic and Colloidal Systems: Asymptotic Laws
- From random walk to single-file diffusion
- Large Deviations in Single File Diffusion
- Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
- Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
- The Exclusion Process: A paradigm for non-equilibrium behaviour
- Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
- Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
- Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications
- Universal Large Deviations for the Tagged Particle in Single File Motion
- Large deviations of a tracer in the symmetric exclusion process
- Universal Long Ranged Correlations in Driven Binary Mixtures
- Large deviation function of a tracer position in single file diffusion
- Order and symmetry-breaking in the fluctuations of driven systems
- Dynamical properties of single-file diffusion
- Vortices in the two-dimensional Simple Exclusion Process
- The crossover from the Macroscopic Fluctuation Theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion
- Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory
- Exact spatial correlations in single-file diffusion
- Long-range fluctuation-induced forces in driven electrolytes
- Generalised density profiles in single-file systems
- Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges
- Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
- Correlations of the density and of the current in non-equilibrium diffusive systems
- Dynamical fluctuations in the Riesz gas
- Variational calculation of transport coefficients in diffusive lattice gases
- A Gaussian theory for fluctuations in simple liquids
- Bulk diffusion in a kinetically constrained lattice gas
- Weak additivity principle for current statistics in d-dimensions
- Duality relations in single-file diffusion
- Joint distribution of currents in the symmetric exclusion process
- Tracer diffusion beyond Gaussian behavior: explicit results for general single-file systems
- Current fluctuations in a semi-infinite line
- Current fluctuations in the Dyson Gas
- Fluctuations in the active Dyson Brownian motion and the overdamped Calogero-Moser model
- Scaling laws for single-file diffusion of adhesive particles
- Semi-infinite simple exclusion process: from current fluctuations to target survival
- Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
- Tracer and current fluctuations in driven diffusive systems
- Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
- Lecture notes on large deviations in non-equilibrium diffusive systems
- Universal scale-free decay of tracer-bath correlations in -dimensional interacting particle systems
- Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
- Single file dynamics of tethered random walkers