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Arrhenius law for interacting diffusive systems

Vishwajeet Kumar1,2, Arnab Pal1,2,*, and Ohad Shpielberg3,4,†

  • 1The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
  • 2Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
  • 3Department of Mathematics and Physics, University of Haifa at Oranim, Kiryat Tivon 3600600, Israel
  • 4Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Abba Khoushy Avenue 199, Haifa 3498838, Israel

  • *Corresponding author: arnabpal@imsc.res.in
  • †ohads@sci.haifa.ac.il

Phys. Rev. E 109, L032101 – Published 6 March, 2024

DOI: https://doi.org/10.1103/PhysRevE.109.L032101

Abstract

Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory—a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.

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