# First passage time distribution of active thermal particles in potentials

@article{Walter2020FirstPT, title={First passage time distribution of active thermal particles in potentials}, author={Benjamin Walter and Gunnar Pruessner and Guillaume Salbreux}, journal={arXiv: Statistical Mechanics}, year={2020} }

We introduce a perturbative method to calculate all moments of the first-passage time distribution in stochastic one-dimensional processes which are subject to both white and coloured noise. This class of non-Markovian processes is at the centre of the study of thermal active matter, that is self-propelled particles subject to diffusion. The perturbation theory about the Markov process considers the effect of self-propulsion to be small compared to that of thermal fluctuations. To illustrate…

## 5 Citations

Run-and-tumble motion in a harmonic potential: field theory and entropy production

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

Run-and-tumble (RnT) motion is an example of active motility where particles move at constant speed and change direction at random times. In this work we study RnT motion with diffusion in a harmonic…

Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states

- MathematicsSciPost Physics
- 2022

We derive universal thermodynamic inequalities that bound from below the moments of first-passage times of stochastic currents in nonequilibrium stationary states of Markov jump processes in the…

Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes

- Economics
- 2021

Benjamin Walter, 2, 3, 4 Gunnar Pruessner, 2 and Guillaume Salbreux 6 Department of Mathematics, Imperial College London, 180 Queen’s Gate, SW7 2AZ London, United Kingdom Centre for Complexity &…

Mean first passage time and absorption probabilities of a Lévy flier on a finite interval: discrete space and continuous limit via Fock space approach

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2021

We have extended the Fock space (FS) approach to address the relevant problem of evaluating the mean first passage time (MFPT) and absorption probabilities of a Lévy random particle in a discrete…

Dissipation bounds the moments of first-passage times of dissipative currents in nonequilibrium stationary states

- Mathematics
- 2021

We derive generic thermodynamic bounds on the moments of first-passage times of dissipative currents in nonequilibrium stationary states. These bounds hold generically for nonequilibrium stationary…

## References

SHOWING 1-10 OF 72 REFERENCES

From first-passage times of random walks in confinement to geometry-controlled kinetics

- Mathematics
- 2014

Multidimensional stationary probability distribution for interacting active particles

- PhysicsScientific reports
- 2015

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative…

First passage time densities in non-Markovian models with subthreshold oscillations

- Mathematics
- 2006

Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process x(t) and particularly the time after which it will reach a certain level xb for the first…

Mean first-passage times of non-Markovian random walkers in confinement.

- MathematicsNature
- 2016

An analytical approach is introduced to calculate the mean first-passage time of a Gaussian non-Markovian random walker to a target in the limit of a large confining volume, and reveals, on the basis of Gaussian processes, the importance of memory effects in first-Passage statistics of non- Markovianrandom walkers in confinement.

Pressure and flow of exponentially self-correlated active particles.

- PhysicsPhysical review. E
- 2017

An exact expression is obtained for the steady-state phase-space density of a single Ornstein-Uhlenbeck Particle confined by a quadratic potential, and the result is used to explore more complex geometries, both through analytical approximations and numerical simulations.

First passage statistics for diffusing diffusivity

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law yet the distribution of particle displacements is strongly…

Mean first-passage times in confined media: from Markovian to non-Markovian processes

- Mathematics
- 2015

We review recent theoretical works that enable the accurate evaluation of the mean first passage time (MFPT) of a random walker to a target in confinement for Markovian (memory-less) and…

Second-order moment of the first passage time of a quasi-Hamiltonian oscillator with stochastic parametric and forcing excitations

- PhysicsJournal of Sound and Vibration
- 2018

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

- Mathematics
- 2017

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as…

Mean first passage time for a class of non-Markovian processes.

- MathematicsChaos
- 2007

The mean first passage time is obtained for CTRW processes with truncated power-law transition time distribution based on the fact that the solutions of the non-Markovian master equation can be obtained via an integral transform from a Markovian Langevin process.