Coarse-grained second order response theory

We will first consider a perturbation theory for Markov processes, expanding expectations of the state at a given time in orders of some small perturbation parameter around equilibrium.

In many physical applications however, it is impossible to observe the full state space, and instead we can only distinguish a finite number of states. This results in a so called coarse grained process given as a function of the underlying Markov process.

We will show that the first order is analogous to the Markovian case and that we can extrapolate the second order from linear terms under certain conditions.

This talk is based on results of my master thesis and joint work with Urna Basu, Peter Sollich and Matthias Krüger arxiv.org/abs/2005.05169 <https://arxiv.org/abs/2005.05169>.