On the ergodicity breaking in well-behaved Generalized Langevin Equations

• DOI: 10.48550/arxiv.2403.05437
• Publication Date: 2024-03-08
• Authors: Giuseppe Procopio; Chiara Pezzotti; Massimiliano Giona
• Keywords: Ergodicity; Langevin equation

The phenomenon of ergodicity breaking stochastic dynamics governed by Generalized Langevin Equations (GLE) in the presence well-behaved exponentially decaying dissipative memory kernels, recently investigated many authors (Phys. Rev. E {\bf 83} 062102 2011; Phys. 98} 062140 2018; Eur. J. B 93} 184 2020), finds, dynamic theory GLE, its simple and natural explanation, related to concept stability. It is shown that occurrence breakdown for kernels falls, general, ouside region realizability, therefore it cannot be observed physical systems.