2026/07/06 by Anonymous, Derek Frydel
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Diffusion and Search Dynamics #cond-mat.soft #cond-mat.stat-mech #physics.bio-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/7pxv-tg3b
published as Phys. Rev. E 114, 024105 (2026)
arxiv created 2026/07/06 · openalex publication_date 2026/07/13 · openalex created_date 2026/07/14 · arxiv updated 2026/08/04 · openalex updated_date 2026/08/04
We study a Brownian particle in a harmonic trap whose stiffness switches between two values with arbitrary waiting-time statistics, leading to semi-Markovian dynamics. To restore Markovianity, we formulate the problem in an enlarged age-structured state space. Using this framework, we obtain steady-state integral equations for the stationary distributions and exact expressions for stationary moments, injected power, and potential energy. In the second part of the paper, we focus on the stochastic-resetting limit, corresponding to a particle alternately released and trapped. By representing the stationary spatial distribution as a superposition of Gaussian states for different effective stiffness (or variance), the problem can be reformulated in variance space, leading to a simplified description amenable to direct analytical treatment.