[@ffs; @valerianiFFS]. Finally we illustrate our procedure on a simple example. In terms of notations and assumptions, we will denote by $\zz$ the location of the system in its state-space $\Omega\subset \RR^d$ (e.g. it could be the positions and velocities of all the atoms in a molecular system, in which case $\zz= (\xx,\vv)$ and $d=6n$ if $n$ is the number of atoms). The specifics of the dynamics of the system are not important except that we assume that (i) its evolution is Markovian and (ii) it is ergodic with respect to a probability density function which we denote by $\varrho(\zz)$. Notice that we do not require detailed balance, i.e. $\varrho(\zz)$ is associated with a nonequilibrium statistical steady state in general.

#### Restricted sampling with flux matching. {#restricted-sampling-with-flux-matching. .unnumbered}

The methods in Refs.  are based on a factorization of the dynamics in which one artificially constrains the system to evolve in a set of cells partitioning state-space in a way that (i) does not bias the dynamics inside the cells and (ii) is consistent with the exact probability fluxes in and out of these cells. In other words, the procedure guarantees that a true unconstrained trajectory of the system can be 