Growth laws and universality in two-temperature induced phase separation: Microscopic and coarse-grained approach.

Two-temperature induced phase separation (2-TIPS) is a phenomenon observed in mixtures of active and passive particles modeled by scalar activity where the temperature of the particle is proportional to its activity. The binary mixture of "hot" and "cold" particles phase separates when the relative temperature difference between hot and cold particles, defined as activity χ, exceeds a density-dependent critical value. The study of kinetics in 2-TIPS, a nonequilibrium phase separation, is of fundamental importance in statistical physics. In this paper, we investigate 2-TIPS kinetics using molecular dynamics (MD) and coarse-grained (CG) modeling in three and two dimensions. The coarse-grained model couples two passive model B equations for hot and cold particles, with coupling terms emulating the energy transfer between them by raising the temperature of cold particles and lowering that of hot particles, a key observation from the MD simulations. MD simulations reveal that, at high densities, phase separation begins immediately after the quench, forming bicontinuous domains rich in hot or cold particles, similar to spinodal decomposition in passive systems. These interconnected domains are also observed in the coarse-grained model for the mixture's critical composition. Both MD and CG models show dynamic scaling of the correlation function, indicating self-similar domain growth. Regardless of dimensionality, both methods report algebraic growth in domain length with a growth exponent of 1/3, known as the Lifshitz-Slyozov exponent, widely observed in passive systems. Our results demonstrate that the universality of phase-separation kinetics observed in passive systems also extends to the nonequilibrium binary mixture undergoing 2-TIPS.