2020/02/13 by Michał Mandrysz, Bartłomiej Dybiec
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Bounded function #Bounding overwatch #Classical mechanics #Computer science #Diffusion and Search Dynamics #Equipartition theorem #Gaussian #Kinetic energy #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Statistical physics #Statistics #White noise #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.102.022105
published as Phys. Rev. E 102, 022105 (2020)
arxiv created 2020/02/13 · openalex publication_date 2020/08/07 · arxiv updated 2020/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper presents analytical and numerical results on the energetics of nonharmonic, undamped, single-well, stochastic oscillators driven by additive Gaussian white noises. The absence of damping and the action of noise are responsible for the lack of stationary states in such systems. We explore the properties of average kinetic, potential, and total energies along with the generalized equipartition relations. It is demonstrated that in frictionless dynamics, nonequilibrium stationary states can be produced by stochastic resetting. For an appropriate resetting protocol, the average energies become bounded. If the resetting protocol is not characterized by a finite variance of renewal intervals, stochastic resetting can only slow down the growth of the average energies but it does not bound them. Under special conditions regarding the frequency of resets, the ratios of the average energies follow the generalized equipartition relations.