  Inverse mass cascade is a key feature of statistically steady state for
self-gravitating collisionless dark matter flow (SG-CFD). Continuous mass
transfer from small to large mass scales (inverse) is formulated. Direct effect
of mass cascade on halo mass function is presented. Mass cascade is local,
two-way, and asymmetric in mass space. Halos inherit/pass their mass from/to
halos of similar size. Two regimes are identified: a propagation range with
scale-independent rate of mass transfer and a deposition range with cascaded
mass consumed to grow halos. Dimensional analysis leads to a power-law mass
function in propagation range with a geometry exponent ${\lambda}$. A
fundamental merging frequency $f_0{\sim}m_p^{\lambda-1}a^{-1}$ is identified,
where $a$ is scale factor. Particle mass $m_p$ can be determined if that
frequency is known. Rate of mass transfer ${\epsilon}_m{\sim}a^{-1}$ is
independent of halo mass, a key feature of propagation range. Typical halos
grow as $m_h{\sim}a^{3/2}$ and halo lifespan scales as ${\sim}m_h^{-\lambda}$.
Chain reaction of mass cascade provides non-equilibrium dark matter flow a
mechanism to continuously release energy and maximize entropy. Continuous
injection of mass ("free radicals") at the smallest scale is required to
sustain the everlasting inverse mass cascade such that total halo mass $M_h$
increases as $a^{1/2}$. These "radicals" might be directly generated at the
smallest Planck scale or by a direct cascade from large to small scales. Entire
mass cascade can be formulated by random walk in mass space, where halos
migrate with an exponential distribution of waiting time. This results in a
heterogeneous diffusion model, where Press-Schechter mass function can be fully
derived without relying on any specific collapse models. A double-$\lambda$
mass function is proposed with different $\lambda$ for two ranges and agrees
with N-body simulations.
