For a pencil-shaped extended medium with Fresnel number equal to 1, we have quantum mechanically derived a description of the initiation of superfluorescence in terms of Maxwell-Bloch equations with a fluctuating source due to the zero-point fluctuations of the vacuum field. By the introduction of classical behavior, these equations are extended to include nonlinear behavior due to decreasing atomic inversion. The principal assumption in the derivation is that the main features of superfluorescence are governed by the interaction of atoms with field modes inside two small solid angles around the pencil axis. The delay ${\ensuremath{\tau}}_{D}$, defined as the time at which the mean-squared tipping angle of the collective Bloch vector attains the value 1, turns out to be given by ${\ensuremath{\tau}}_{D}=(\frac{{\ensuremath{\tau}}_{R}}{4}){[\mathrm{ln}{(2\ensuremath{\pi}N)}^{\frac{1}{2}}]}^{2}$, where ${\ensuremath{\tau}}_{R}$ is the radiation time for collective decay and
N is the number of atoms. The corresponding effective initial tipping angle roughly equals
(N)212. A Fokker-Planck equation is derived to describe the statistics of the initial development of the tipping angle. The variance $\ensuremath{\Delta}{\ensuremath{\tau}}_{D}$ of the delay of the superfluorescence pulse satisfies approximately $\ensuremath{\Delta}{\ensuremath{\tau}}_{D}=\frac{2.3}{\mathrm{ln}N}$. A brief comparison with previous treatments of superfluorescence is given.
The self-organization process of superfluorescence can be explained clearly basing on the thermodynamics. The present paper includes three parts: 1) the equations of superfluorescence radiation and heat transform cetion are derived, and their transient processes are analysed; 2) the possibility of the generation of superfluorescence is theoretically verified by the analysis of the linear stability of the thermo-dynamic Maxwell-Bloch equations, and the coherent process of superfluorescence is analysed by the temporal coherence function of the field of radiation obtained: 3) the effective initial tipping angle θ0 and the delay time τD are derived from the fluctuation in statistical thermodynamics. Numerical results are in good agreement with those accepted up to now.