## 3 Discussion  
The non-equilibrium dynamics observed here are significantly different from those observed in, e.g., simple metals. In such systems, optical excitation generates a non-equilibrium distribution of electrons which thermalizes on the 10-100 fs timescale [36; 37; 38; 39]. The resulting high-temperature distribution function subsequently relaxes on the few ps timescale due to electron-phonon interaction [40; 41; 42], leaving the system behind in a new equilibrated state that can be characterized by one uniform, transient temperature. Here, we observe a persisting non-equilibrium situation in the electronic subsystem on the ps timescale (Figure 3b), when a majority of electronic excess energy is  
Figure 4: (**a**) Transient spectral intensity in a small energy window (\(E-E_{F}=-65\)... \(-45\) meV) from which the CDW amplitude mode dynamics can be extracted. Dashed lines are fits to the data, assuming a damped single oscillatory component \(I(t)=A\cdot exp(-t/\tau)\cdot cos(\omega t+\varphi)+B\) with a frequency of 2.5 THz. Typical goodness of fits are \(\chi^{2}=\)0.15-0.16; (**b**) shows the amplitude \(A\) of the oscillation as a function of fluence. The solid black line is the result of the modelling already shown in Figure 3a. Vertical dashed lines indicate the fluence range in which saturation occurs. already transferred to the lattice [20; 33]. A particular finding is that the recovery of this non-equilibrium state is only partial, as the LHB intensity is not fully restored after several ps. Similar persisting, transient states were also observed during the structural response of photo-excited 1\(T\)-TaS\({}_{2}\)[35], where the formation of a long-living (>10 ps), quasi-equilibrated lattice state was found to occur on timescales comparable to the LHB recovery times discussed here. Our data clearly show a link between the CDW periodic lattice distortion and short-range electronic correlations, as both signatures show the same saturating behavior, see Figures 3a and 4b. From our experimental findings we conclude on a hierarchy of time scales that we discuss in a localized picture:  
(i) The optical excitation of the electronic subsystem results in a prompt collapse of the Mott state [24] which is reflected by a transient reduction of the LHB intensity. In a simplified scheme, these localized excitations of ground state carriers result in the generation of spatially randomly distributed \"metallic\" clusters which are similar to the discommensurations found in the higher temperature phases and are reflected by a partial filling of the formerly gapped spectral region around \(E_{F}\). This situation is not stable as evident from the different ordered equilibrium structures that exhibit well-defined long-range configurations of the lattice. These clusters can be interpreted as defects of the CDW and locally trigger the excitation of the CDW amplitude mode phonon. We assume the excitation of the CDW amplitude mode phonon to be local, e.g., on single clusters. This assumption is justified, as the corresponding optical phonon branches are of narrow band width [43; 44], which allows for our experimentally observed dephasing times of >10 ps (Figure 4a). On these ultrashort time scales (<100 fs), a majority of excess energy is stored in the electronic subsystem. (ii) The electronic excess energy is largely transferred to the lattice system within few 100 fs due to the incoherent excitation of phonons. While the electronic system is almost thermalized [20], the lattice system is in a non-equilibrium state as the CDW amplitude phonon mode is still highly populated. (iii) The LHB signature recovers due to the reformation of the Mott state on the 1 ps time scale.