# A martingale approach to time-dependent and time-periodic linear response in Markov jump processes

@inproceedings{Faggionato2022AMA, title={A martingale approach to time-dependent and time-periodic linear response in Markov jump processes}, author={Alessandra Faggionato and Vittoria Silvestri}, year={2022} }

. We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a ﬁnite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the perturbation we show that the perturbed process does not explode almost surely and we study the linear response (LR) of observables and additive functionals. When the unperturbed process is stationary, the above LR formulas become computable in terms of the steady…

## References

SHOWING 1-10 OF 27 REFERENCES

### Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing

- Physics, Mathematics
- 2015

We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some…

### The technique of the exponential change of measure for Markov processes

- Mathematics
- 2000

It is demonstrated that the process X (t) is a Markov process on the probability space (U, F, fF tg, ~ P), and the extended generator ~ A is found and provided sufficient conditions under which D(~ A) 1⁄4 D(A).

### Piecewise-deterministic Markov Processes: A General Class of Non-diffusion Stochastic Models

- Mathematics, Computer Science
- 2018

Stochastic calculus for these stochastic processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper.

### An update on the nonequilibrium linear response

- Mathematics
- 2013

The unique fluctuation–dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is ‘analytic’, which,…

### The Einstein relation for the displacement of a test particle in a random environment

- Mathematics
- 1994

### Response Theory: A Trajectory-Based Approach

- PhysicsFrontiers in Physics
- 2020

We collect recent results on deriving useful response relations also for non-equilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space.…

### Steady States, Fluctuation–Dissipation Theorems and Homogenization for Reversible Diffusions in a Random Environment

- Mathematics
- 2018

Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe…

### Einstein relation and linear response in one-dimensional Mott variable-range hopping

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2019

We consider one-dimensional Mott variable-range hopping with a bias, and prove the linear response as well as the Einstein relation, under an assumption on the exponential moments of the distances…

### Onsager-Machlup Theory and Work Fluctuation Theorem for a Harmonically Driven Brownian Particle

- Mathematics, Physics
- 2007

We extend Tooru-Cohen analysis for nonequilibrium steady state (NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive…