The effect of the environment on the torsion of the system is to slightly reduce its kinetic energy from the 2D to the 2D + 23BM simulation, which is expected since the additional degrees of freedom, modelled here as a bath of harmonic oscillators, is that of stabilizing the photo-product in the trans configuration once it is formed. As it is observed in general in all results reported in Figs. and, including a large number of bath modes reduces the deviation between CT-TSH and TSH-ED (at least, up to 300 fs): when comparing the kinetic energy along the coupling mode for a small number of bath modes, CT-TSH and TSH-ED show a slightly different behavior, which is, instead, "washed out" by the presence of the environment. The coupled-trajectory approach, by contrast to the independent-trajectory approach, can be thought as preserving some degree of quantumness in its description of nuclear dynamics, since the trajectories, being coupled, behave as belonging to a single entity, i.e., the quantum nuclear density. This is the feature that, when accounted for in the electronic evolution equation, correctly accounts for quantum decoherence. When the number of degrees of freedom of the bath increases, the system is coupled to a large number of modes and encounters a large number of energy dissipation and decoherence channels, which make the system somehow more "classical" than when it is isolated.