Equilibration to the steady state for a wide class of Luttinger liquid ballistic weakly linked tunnel contacts is extensively studied. Quantum fluctuations of tunnel current are considered in all orders in tunnel coupling and out of the equilibrium in the time domain. Especially, two important mathematical statements: Self-equilibration (SE-)theorem and Self-equilibration (SE-)lemma on the exact re-exponentiation of thermal average from the Keldysh-contour-ordered evolution operator for arbitrary weakly linked Luttinger liquid tunnel contact are proven. Demonstrated proof of SE-theorem and SE-lemma represents first evidence of a novel emergent phenomenon of ”self-equilibration” in the dynamics of quantum fluctuations of electron transport through ballistic tunnel junctions. This phenomenon and all related real-time full counting statistics are shown to be much more general as compared to the usual Levitov–Lesovik scattering approach for the non-interacting electrons, though SE-theorem also contains known results obtained within the Levitov–Lesovik scattering approach as corresponding limiting case for lowest order cumulants at g=1. As the result, corresponding differential equation of ”self-equilibration” for time-dependent Keldysh partition function of tunnel contact is derived and explained. It is shown that proven SE-theorem can be considered also as the dynamical version of well-known Jarzynski equality for the tunnel electron transport out of the equilibrium. As the result, for arbitrary weakly linked tunnel junction model of interest the exact time-dependent cumulant generating functional is derived being valid at arbitrary electron–electron repulsion in the Luttinger liquid leads of the junction, arbitrary temperature and arbitrary bias voltage. Respective general formula in its long-time asymptote turns into a non-perturbative Luttinger liquid generalization of the Levitov–Lesovik type of detailed balance formula for cumulant generating function. As the consequence of obtained results, a universal character of self-equilibration of tunnel current in one-dimensional weakly linked tunnel junctions is revealed and studied on the level of non-equilibrium Fano factor. As well, a new measure of disequilibrium in such systems – the ”steady flow” rate – is also introduced and discussed.