Dynamical stationarity as a result of sustained random growth

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast-growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationary distributions is a generalization of the fluctuation-dissipation theorem. Entropic distance evolution is given for such systems. We reconstruct distributions obtained for growing networks, particle production, scientific citations, and income distribution.