Exactly solvable diffusions from space-time transformations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912470646390784 |
|---|---|
| author | Di Bello, Costantino Roldán, Édgar Metzler, Ralf |
| author_facet | Di Bello, Costantino Roldán, Édgar Metzler, Ralf |
| contents | We consider a general one-dimensional overdamped diffusion model described by the Itô stochastic differential equation (SDE) ${dX_t=μ(X_t,t)dt+σ(X_t,t)dW_t}$, where $W_t$ is the standard Wiener process. We obtain a specific condition that $μ$ and $σ$ must fulfil in order to be able to solve the SDE via mapping the generic process, using a suitable space-time transformation, onto the simpler Wiener process. By taking advantage of this transformation, we obtain the propagator in the case of open, reflecting, and absorbing \emph{time-dependent\/} boundary conditions for a large class of diffusion processes. In particular, this allows us to derive the first-passage time statistics of such a large class of models, some of which were so far unknown. While our results are valid for a wide range of non-autonomous, non-linear and non-homogeneous processes, we illustrate applications in stochastic thermodynamics by focusing on the propagator and first-passage-time statistics of isoentropic processes that were previously realized in the laboratory with Brownian particles trapped with optical tweezers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exactly solvable diffusions from space-time transformations Di Bello, Costantino Roldán, Édgar Metzler, Ralf Statistical Mechanics We consider a general one-dimensional overdamped diffusion model described by the Itô stochastic differential equation (SDE) ${dX_t=μ(X_t,t)dt+σ(X_t,t)dW_t}$, where $W_t$ is the standard Wiener process. We obtain a specific condition that $μ$ and $σ$ must fulfil in order to be able to solve the SDE via mapping the generic process, using a suitable space-time transformation, onto the simpler Wiener process. By taking advantage of this transformation, we obtain the propagator in the case of open, reflecting, and absorbing \emph{time-dependent\/} boundary conditions for a large class of diffusion processes. In particular, this allows us to derive the first-passage time statistics of such a large class of models, some of which were so far unknown. While our results are valid for a wide range of non-autonomous, non-linear and non-homogeneous processes, we illustrate applications in stochastic thermodynamics by focusing on the propagator and first-passage-time statistics of isoentropic processes that were previously realized in the laboratory with Brownian particles trapped with optical tweezers. |
| title | Exactly solvable diffusions from space-time transformations |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2503.16090 |