2024/01/17 by Paul Nikolaev, Nikolaev, Paul, David J. Prömel +1
Physics and Astronomy · #35D30 #35Q70 #60K35 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2401.08938
openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method under the moderated interaction scaling introduced by Oeschläger, and the propagation of chaos in probability. The result includes the case that the interaction force does not need to be a potential field. Furthermore, if the interaction force is a potential field, with a convolutional structure, then the developed estimate also provides the modulated energy estimates. Moreover, we demonstrate propagation of chaos for large stochastic systems of interacting particles and discuss possible applications to various interacting particle systems, including the Coulomb interaction case.