2019/01/31 by Tal Agranov, P. L. Krapivsky, Baruch Meerson
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Formalism (music) #Geology #Mathematical analysis #Mathematics #Physics #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Residence time (fluid dynamics) #Singularity #Statistical physics #Statistics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.99.052102
published as Phys. Rev. E 99, 052102 (2019) · 15 pages, 8 figures
arxiv created 2019/04/07 · openalex publication_date 2019/05/02 · arxiv updated 2019/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The time that a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently, the joint occupation-time statistics of an ensemble of noninteracting particles was addressed using the single-particle statistics. Here we employ the macroscopic fluctuation theory (MFT) to study the occupation-time statistics of many interacting particles. We find that interactions can significantly change the statistics and, in some models, even cause a singularity of the large-deviation function describing these statistics. This singularity can be interpreted as a dynamical phase transition. We also point out to a close relation between the MFT description of the occupation-time statistics of noninteracting particles and the level 2 large deviation formalism which describes the occupation-time statistics of a single particle.