  Experiments and simulations have established that dynamics in a class of
living and abiotic systems that are far from equilibrium exhibit super
diffusive behavior at long times, which in some cases (for example evolving
tumor) is preceded by slow glass-like dynamics. By using the evolution of a
collection of tumor cells, driven by mechanical forces and subject to cell
birth and apoptosis, as a case study we show theoretically that on short time
scales the mean square displacement is sub-diffusive due to jamming, whereas at
long times it is super diffusive. The results obtained using stochastic
quantization method, which is needed because of the absence of
fluctuation-dissipation theorem (FDT), show that the super-diffusive behavior
is universal and impervious to the nature of cell-cell interactions.
Surprisingly, the theory also quantitatively accounts for the non-trivial
dynamics observed in simulations of a model soap foam characterized by creation
and destruction of spherical bubbles, which suggests that the two
non-equilibrium systems belong to the same universality class. The theoretical
prediction for the super diffusion exponent is in excellent agreement with
simulations for collective motion of tumor cells and dynamics associated with
soap bubbles.
