We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of 258 Fm can be well reproduced using simple assumptions on the quantum collective phase-space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory with pairing. This approach goes beyond mean-field by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation as well as pre-scission particle emission, are obtained. We conclude that fluctuations of TKE and mass are triggered by quantum fluctuations.PACS numbers: 21.60. Jz, 24.75.+i, 25.85.Ca, 27.90.+b The dynamical modeling of a nuclear Fermi quantum droplet that spontaneously breaks into two pieces represents one of the most exciting challenges of nuclear physics today. Beside its description, a deeper microscopic understanding of spontaneous fission (SF) is of great importance to form the heaviest elements at the frontier of the nuclear chart [1][2][3] or to further improve our knowledge about the competition between the r-process and fission during the primordial nucleosynthesis [4]. Motivated also by its importance in nuclear energy production, intensive experimental efforts have been made to accumulate precise measurements [5][6][7][8][9]. In recent years, an increasing effort was made to remove empirical ingredients that are employed in macroscopic modeling of fission and use microscopic theories [10,11]. The nuclear Density Functional Theory (DFT) is a suitable starting point to describe some aspects related to the large amplitude collective motion (LACM). A minimal information obtained from DFT is the adiabatic collective energy landscape [11]. One challenge to describe spontaneous fission (SF) is the necessity to explicitly treat the evolution as a quantum dynamic in collective space. Progresses have been made with the Time-Dependent Generator Coordinate Method (TDGCM) [12][13][14]. This theory by treating quantally collective degrees of freedom (DOF) is promising. However, the adiabatic assumption often made becomes critical especially close to scission [15]. Dissipation of the collective motion into internal excitations also plays a key role to understand the excitation energy and kinetic energy sharing during fragments separation [16]. Understanding this dissipation requires to include many-body states beyond the adiabatic limit [17]. It is yet unclear how the pre-scission neutron and proton emissions can be incorporated in the TDGCM.The nuclear time-dependent DFT (TDDFT) overcomes some of these limitations. With recently developed symmetry unrest...