Phase Instabilities in Biochemically Open Active Multicomponent Mixtures

Understanding the phase behavior of biological mixtures has attracted significant research interest, particularly in the context of liquid-liquid phase separation. These systems are inherently high-dimensional and complex, encompassing thousands of interacting species and biochemical reactions, and are further complicated by the violation of detailed balance typically due to biochemical openness and intrinsic activity. In this work, we present a general framework to tackle these high-dimensional nonequilibrium systems by building upon reaction-diffusion equations, open biochemical reaction networks, and non-Hermitian random matrix theory. We discuss how the interplay between biochemical reactions and activity influences the onset of phase instabilities and modulates characteristic timescales. Furthermore, we propose a potential conceptual linkage to the behavior of gated recurrent neural networks, offering avenues for cross-disciplinary insights.