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Inverse mass cascade is a key feature of statistically steady state forself-gravitating collisionless dark matter flow (SG-CFD). Continuous masstransfer from small to large mass scales (inverse) is formulated. Direct effectof 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/tohalos of similar size. Two regimes are identified: a propagation range withscale-independent rate of mass transfer and a deposition range with cascadedmass consumed to grow halos. Dimensional analysis leads to a power-law massfunction in propagation range with a geometry exponent ${\lambda}$. Afundamental 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 thatfrequency is known. Rate of mass transfer ${\epsilon}_m{\sim}a^{-1}$ isindependent of halo mass, a key feature of propagation range. Typical halosgrow 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 amechanism to continuously release energy and maximize entropy. Continuousinjection of mass ("free radicals") at the smallest scale is required tosustain the everlasting inverse mass cascade such that total halo mass $M_h$increases as $a^{1/2}$. These "radicals" might be directly generated at thesmallest Planck scale or by a direct cascade from large to small scales. Entiremass cascade can be formulated by random walk in mass space, where halosmigrate with an exponential distribution of waiting time. This results in aheterogeneous diffusion model, where Press-Schechter mass function can be fullyderived without relying on any specific collapse models. A double-$\lambda$mass function is proposed with different $\lambda$ for two ranges and agreeswith N-body simulations.

Inverse mass cascade in dark matter flow and effects on halo mass functions