The noisy Pais–Uhlenbeck oscillator

Urenda-Cázares, E.; Espinoza, P.; Gallegos, A.; Jaimes-Reátegui, R.; Macías‐Díaz, Jorge E.; Vargas-Rodríguez, Héctor

doi:10.1007/s10910-018-0966-6

Cited by 4 publications

(3 citation statements)

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“…With the aid of these two equations, the quantities of work, heat, and entropy can be well defined on microscopic trajectories. In this paper, we have derived the Langevin equation (29) and its corresponding Fokker-Planck equation (35) for a HDD Brownian particle. It is valuable for us to extend current stochastic thermodynamics to the case of HDD based on these two equations.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Following Reichl's derivation [27] of the Fokker-Planck equation from the Langevin equation, we can derive the Fokker-Planck equation corresponding to the Langevin equation (29) [equivalently, Eqs. ( 19) and ( 31)] with HDD from Eqs.…”

Section: Fokker-planck Equation With Hddmentioning

confidence: 99%

“…A oscillator described in the above equation is named as stochastic Pais-Uhlenbeck oscillator. To the best of our knowledge, Nesterenko first discussed the Pais-Uhlenbeck oscillator with a damping term [28], while Urenda-Cázares et al discussed the Pais-Uhlenbeck oscillator with a noise term [29]. They wrote the corresponding equations phenomenologically without microscopic derivations.…”

Section: Stochastic Pais-uhlenbeck Oscillatormentioning

confidence: 99%

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Brownian motion of a particle with higher-derivative dynamics

Tu¹

2023

Preprint

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The Brownian motion of a particle with higher-derivative dynamics (HDD) coupling with a bath consisting of harmonic oscillators is investigated. The Langevin equation and corresponding Fokker-Planck equation for the Brownian motion of the HDD particle are derived. As a case study, we particularly consider a stochastic Pais-Uhlenbeck oscillator. It is found that the Boltzmann distribution is pathological while this distribution is the steady solution to the Fokker-Planck equation.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Fokker-planck Equation With Hddmentioning

confidence: 99%