Macroscopic fluctuation theory from a Lagrangian viewpoint and the Schrödinger problem

2025/06/27 by Lorenzo Bertini, Davide Gabrielli, Bertini, L. +3
Mathematics · Physics and Astronomy · #60F10 #60K35 #82C22 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Probability (math.PR) #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2506.22085

openalex publication_date 2025/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate the Schrödinger problem for interacting particle systems in the hydrodynamical regime thus extending the standard setting of independent particles. This involves the large deviations rate function for the empirical measure which is in fact a richer observable than the hydrodynamic observables density and current. In the case in which the constraints are the initial and final density, we characterize the optimal measure for the Schrödinger problem. We also introduce versions of the Schrödinger problem in which the constraints are related to the current and analyze the corresponding optimal measures.

Citations

• Exact solutions to macroscopic fluctuation theory through classical integrable systems
• Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Concurrent Donsker-Varadhan and hydrodynamical large deviations
• Asymptotic Behavior of Stochastic Currents under Large Deviation Scaling\n with Mean Field Interaction and Vanishing Noise
• The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
• Tagged particle in single-file diffusion
• Large Deviation Principle for Interacting Brownian Motions
• Macroscopic fluctuation theory
• Nonequilibrium fluctuations for a tagged particle in mean-zero one-dimensional zero-range processes

Related

• Macroscopic Fluctuation Theory versus large-deviation-induced GENERIC
• Fluctuations for some non-stationary interacting particle systems via Boltzmann-Gibbs Principle
• Full counting statistics after quantum quenches as hydrodynamic fluctuations
• Notes about the Macroscopic Fluctuating Theory
• Interacting particle systems: hydrodynamic limit versus high density limit