Phenomenological Scaling Crossovers in Non-Equilibrium Critical Dynamics

Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied, the theoretical framework for scaling crossovers between distinct dynamical regimes remains underdeveloped. In this work, we propose a phenomenological approach to describe dynamic scaling crossovers in reaction-diffusion systems, utilizing a Bernoulli differential equation with time-dependent reaction coefficients. Under a new scaling hypothesis for spatial fluctuations, we analytically derive five universal power-law crossover functions. These solutions accurately describe experimental observations of absorbing phase transitions in turbulent liquid crystals and reaction-diffusion crossovers in exciton-exciton recombination, revealing possible mechanisms associated with many-body correlations and two-component dynamics. These findings suggest the existence of universal scaling laws governing the transition between different dynamical states, motivating further studies using field-theoretic approaches and renormalization group analyses.