Restriction and mixing properties of interacting particle systems with unbounded range

We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many interacting particles. Moreover, we also provide non-asymptotic quantitative bounds on the spatial decay of correlations at times $t>0$ and then apply these results to show that interacting particle systems on $\mathbb{Z}$ whose interaction strengths decays exponentially fast cannot spontaneously break the time-translation symmetry, neither in the strong, nor in the weak sense.