random walker, and by applying our method to a dissipative transverse field Ising model [@Ates2012], known to display metastability [@Rose2016].

Reset Markov processes {#ResetMarkov}
======================

We consider a classical stochastic process evolving according to a continuous-time Markov chain. The master equation describing the evolution of the probability $P(C,t)$ for the process to be in state $C$ at time $t$ is given by $$\partial_t P(C,t)=\sum_{C'\neq C}W(C'\rightarrow C)P(C',t)-R(C)P(C,t),$$ where $W(C'\rightarrow C)$ is the transition rate from $C'$ to $C$ and $$R(C)=\sum_{C'\neq C}W(C\rightarrow C')$$ is the escape rate from $C$. Following the notation commonly used in physics [@schutz2001], this can be written more compactly as $$\label{MasterEq}
\partial_t \ket{P(t)} = {\mathcal{L}}\ket{P(t)},$$ where $$\ket{P(t)}=\sum_C P(C,t)\ket{C}$$ is the probability vector expressed in terms of ket states $\ket{C}$, such that $\left\langle C|C' \right\rangle = \delta_{CC'}$, and $${\mathcal{L}}=\sum_{C,C'\neq C}W(C\rightarrow C')\ket{C'}\bra{C}-\sum_C R(C)\ket{C}\bra{C}$$ is the master operator.

Since this operator is non-Hermitian, it has two sets of eigenvectors, right and left, given by $${\mathcal{L}}\ket{r_i}=\lambda_i\ket{r_i}$$ and $$\bra{l_i}{\mathcal{L}}=\lambda_i\bra{l_i},$$ respectively. These two sets of eigenvectors form a complete basis, are dual to each other, and can be normalised in a such a way that $\left\langle l_i | r_j \right\rangle=\delta_{ij}$.

We assume here that the process is ergodic and, therefore, that it has a 