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PreprintCC BY 4.0arXiv

Non-stationary Statistics and Energetics of Brownian Motion under Stochastic Harmonic Confinement

  • Deepak Gupta
  • Sabine H. L. Klapp
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Abstract

We investigate the positional statistics and thermodynamic properties of a Brownian particle confined in a Harmonic trap. The stiffness of the particle fluctuates in time as the square of the Brownian process. First, in the absence of a thermal bath, we investigate the probability density function of the position of the particle at time t. Then, we provide an expression to compute the nth positional moment. We evaluate the first four positional moments and discuss their asymptotic behavior in the long-time limit. In contrast to previously studied models of fluctuating stiffness, the current model describes a non-stationary process. Furthermore, we provide the exact expression for the average work performed on the system and the average heat exchanged by the particle with the bath. Their long time behavior again reflects the non-stationary nature of the process. Our theoretical predictions are supported by numerical simulations.

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Cite

BibTeXRIS
BibTeX
@misc{gupta2026nonstationary,
  title = {{Non-stationary Statistics and Energetics of Brownian Motion under Stochastic Harmonic Confinement}},
  author = {Deepak Gupta and Sabine H. L. Klapp},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33751},
  eprint = {2609.33751},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33751},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-stationary Statistics and Energetics of Brownian Motion under Stochastic Harmonic Confinement
AU  - Deepak Gupta
AU  - Sabine H. L. Klapp
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33751
UR  - https://arxiv.org/abs/2609.33751
AB  - We investigate the positional statistics and thermodynamic properties of a Brownian particle confined in a Harmonic trap. The stiffness of the particle fluctuates in time as the square of the Brownian process. First, in the absence of a thermal bath, we investigate the probability density function of the position of the particle at time t. Then, we provide an expression to compute the nth positional moment. We evaluate the first four positional moments and discuss their asymptotic behavior in the long-time limit. In contrast to previously studied models of fluctuating stiffness, the current model describes a non-stationary process. Furthermore, we provide the exact expression for the average work performed on the system and the average heat exchanged by the particle with the bath. Their long time behavior again reflects the non-stationary nature of the process. Our theoretical predictions are supported by numerical simulations.
ER  -