Work

Macroscopic fluctuation theory from a Lagrangian viewpoint and the Schrödinger problem

Year: 2026

Type: article

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.

Source: Rendiconti Lincei Matematica e Applicazioni

DOI: 10.4171/rlm/1096

Authors: Lorenzo Bertini, Davide Gabrielli, Giovanni Jona-Lasinio

Institutions: Sapienza University of Rome, University of L'Aquila

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, Agence Nationale de la Recherche, Ministero dell’Istruzione, dell’Università e della Ricerca, Ministero degli Affari Esteri e della Cooperazione Internazionale

Awards: G3229954312, G3574577584, G5296751580